263 items are filed under this topic.








Gauss' Addition of whole numbers. 
20180430 

From Brad: I found this on your site. Question: what is the sum of the first 100 whole numbers??
Is there a different formula if the numbers begin at a number other than one? For example
What is the series I want to add is goes from 7  53? Answered by Harley Weston. 





A puzzling sequence 
20171219 

From Alan: My son has the following sequence to work out the formula for the nth term (and fing 5th and 6th terms) and I have tried a variety of ways but can't help!
1/2, 5/6, 1, 11/10
I have converted all to 15/30, 25/30, 30/30, 33/30 and so think the next two terms are 37/30 and 45/30 but I have no idea how to prove or if I am right!
Any help appreciated. Answered by Penny Nom. 





An arithmetic sequence 
20171130 

From yo: x; 2x+1; 11 are three consecutive terms of an arithmetic sequence.calculate x Answered by Penny Nom. 





An alphabetic sequence 
20170917 

From malik: find the letter of the following series....?
ZOTTFFSSE Answered by Penny Nom. 





An arithmetic sequence 
20170717 

From abbi: hi there im a student in 11 grade
ive been trying to do this task but i have no idea how to do it
the question is
Find the common difference and the n^th term of the arithmetic sequence if the first term is 4 and the twentieth sum of the terms is 1030 Answered by Penny Nom. 





Successive Differences 
20170406 

From Twaha: Please find the equation of the sequence 1 2 4 7 11 16 22 Answered by Penny Nom. 





A pattern rule for a sequence 
20161028 

From Grace: Here's a Grade 7 question, we need to find the pattern rule:
1  1
2  3
3  6
4  10
......
It may involve exponents, but we can't seem to figure it out.
thank you.
Grace. Answered by Penny Nom. 





Two sequences 
20160820 

From Ting: The first four terms of a sequence are 4, 20, 56 and 120. By comparing with the nth term of sequence 1,5,14 and 30 which is 1/6n(n+1)(2n+1), find a formula for nth term. Can you precisely show out how you do this questions ( with the steps please) Answered by Penny Nom. 





The sequence 13 17 23 27 33 37 
20160729 

From Shriya: The first term of a sequence is 13.
The following terms are found by alternately adding 4 and 6 to the previous term.
The first six terms are 13 17 23 27 33 37.
Find the 80th term. Answered by Penny Nom. 





Which term of this sequence has value 8? 
20160720 

From Lauren: Hi there
Which term in the sequence 2; 5/3; 4/3 ; 1; ... has a value of 8.
Since term 2 and 3 of this sequence contain fractions which can be converted to recurring decimals. What is the best way to work out the common difference here.
I do however understand that to work out the nth term of an arithmetic series, the following formula Tn = a + (n1)d. In this series a = 2 Answered by Penny Nom. 





A geometric progression 
20160303 

From Pauline: A woman measures the height of her child at birth and at monthly intervals afterwards.The child's height increases by 5% per month. Find the number of measurements she has made before the child's height is twice what it was at birth Answered by Penny Nom. 





Which term of the series 2+7+12+...is 152? 
20160201 

From francis: whice term of the series 2+7+12+...is 152? Answered by Penny Nom. 





A sequence 
20160105 

From Mia: the next three terms in each sequence. 0.4, 0.54, 0.68, 0.82, Answered by Penny Nom. 





The sequence 1,2,4,7,11,16... 
20151015 

From HEMANT: what is the next term in the sequence : 1,2,4,7,11,16,? Answered by Penny Nom. 





The nth term 
20150704 

From ujjal: What is the nth term in the order 6,8,10.... Answered by Penny Nom. 





A geometric sequence 
20150419 

From Delfina: In a geometric sequence the second term is 15 and the fifth term is 405. Find the sum of the first eight terms Answered by Penny Nom. 





Some nondecreasing sequences 
20150413 

From Sky: Hi I'm a Student and i'll try my best to state the problem perfectly.
The number of nondecreasing sequences of size at least 1 and at most N,
such that each element of the sequence lies between L and R, both inclusive.
Eg: N=1 L=4 R=5
ans= 2. [{4},{5}]
N=3 L=4 R=6
ans= 19. [{4},{5},{6},{4,4},{4,5},{4,6},{5,5},{5,6},{6,6}
{4,4,4},{4,4,5},{4,4,6},{4,5,5},{4,5,6},{4,6,6},{5,5,5},{5,5,6},{5,6,6}
,{6,6,6}] Answered by Claude Tardif. 





1,4,9,61,52,___ 
20150121 

From Mubashir: 1,4,9,61,,52,___,84,___,18,1,121,___
please tell me its formula and also that rule that is being applied here like adding 3 or subtracting 5 etc. Answered by Walter Whiteley. 





A sequence 
20150113 

From cyaz: write a rule for each sequence then find next 3 terms for 7/8, 3 1/8, 5 3/8 Answered by Penny Nom. 





Find the nth term 
20141026 

From Kenneth: According to the pattern of the following sequence. Find it's nth term:
3,9,27,81,243,.......... Answered by Penny Nom. 





The sum of the first 50 terms of an arithmetic progression 
20140726 

From Joshua: Hello ...my is Joshua...I'm a grade 11 student...I got a question
Calculate the sum of the first 50 terms of an arithmetic progression: 112:98:84 Answered by Penny Nom. 





9,4,6,8,3,... 
20140331 

From Alynna: You are given the following pattern: 9,4,6,8,3,...
Create a formula for the nth figure.
I have trouble finding the formula, I need help trying to find it. Answered by Penny Nom. 





An arithmetic sequence 
20140320 

From Xabiso: The 10th term of an arithmetic sequence is 28 and the 7th term is 19. Calculate the common difference and the first term of the sequence. Answered by Penny Nom. 





A sequence 
20140210 

From Joshua: hello..the question I have today is... A sequence... 1,5,14,30,55,91 find the general terms. Answered by Penny Nom. 





A sequence 
20140130 

From joshua: hi...really struggle with one question that the teacher gave us...
The sequence is 1,2,1,5,8,1,11,___,___ Answered by Penny Nom. 





An arithmetic sequence 
20140106 

From paris: find the twentyfifth term of an arithmetic sequence whose first term is 12 and whose common difference is 6 Answered by Penny Nom. 





Find the next 3 terms of the sequence 
20131219 

From Lanelyn: Find the next 3 terms of the sequence 2,3,9,23,48,87,__,__,__ Answered by Robert Dawson. 





The sum of all whole numbers from 1 to X 
20130906 

From Tim: How do I develop a rule for the sum of all whole numbers from 1 to X when I have no idea how to do this Answered by Penny Nom. 





A sequence or a series? 
20130905 

From Rahul: Whether the following sequence is increasing or decreasing? I even do not kow whether to call it a sequence or not. an = (1/(1+n))+(1/(2+n))+....+(1/(n+n)).
I am confused. It looks like a series to me. Please help.
Regards,
Rahul Answered by Robert Dawson. 





A geometric sequence 
20130716 

From Relebohile: Find the n^th term of 3,6,9,12,24,48... Answered by Penny Nom. 





Write a rule for the sequence 
20130220 

From Angelia: Write a rule for the sequence. Then, find the unknown term. 1 3/8, 1 ¾, 2 1/8, _______, 2 7/8 Think: The pattern is increasing. Add 1/6 to find the next term. Rule: _______________ Answered by Penny Nom. 





The nth term of a sequence 
20121019 

From Emily: I don't understand how to do this question:
Nth term for 9, 7, 5, 3, 1
Is there a fast way to do nth term for this question? Or in fact any question? Answered by Penny Nom. 





An arithmetic progression 
20120822 

From A student: the 3rd term of an A.PPP is 10 more than the first term while the 5th term is 15 more than the second.find the sum of the 8th and 15th terms if the 7th term is 7 times the first term. Answered by Penny Nom. 





A cylinder is to be filled with peas. 
20120612 

From Silje: Hi! How can I solve the following question without the use of a calculator?
"A cylinder is to be filled with peas. It is done like this: At 12:00 o'clock you put 1 pea in, at 12:01 you put 2 peas in, at 12:02 you put 4 peas in, at 12:03 you put 8 peas in, and so on.
This continues until 14:00 o'clock (two hours later), when the last peas are put in and the cylinder is full. At what time is the cylinder half full?" Answered by Robert Dawson. 





A geometric sequence 
20120610 

From vicki: The sum of the first three terms of a geometric sequence of positive integers is equal to seven times the first term, and the sum of the first four terms is fortyfive. What is the first term of the sequence? Answered by Penny Nom. 





The nth term 
20120505 

From Justin: Which expression can be used tofind the nth term in this sequence?
94,75,56,37,18,.....
My choices are
A. 19n=113 B. 21n+115
C. 19+75 D. 21n+73
Please explain how to get the correct answer. I think it is A. but I am not sure, Answered by Penny Nom. 





A geometric sequence 
20120224 

From Camille: Find x if the sequence 5,10,x+2 is geometric. Answered by Penny Nom. 





A tree growth modelled by a geometric series 
20120208 

From Steph: Hi I am really struggling with this question please help !!!!
a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year.
assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence.
A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres Answered by Penny Nom. 





Three consecutive terms of an arithmetic sequence 
20111030 

From Juliette: Find X when x, 1/2x + 7, 3x 1 are consecutive terms of an arithmetic sequence. Answered by Penny Nom. 





A sequence 
20110814 

From intesar: how do i figure this out 0,1/6,2/9,3/12 Answered by Penny Nom. 





The third term of a sequence 
20110813 

From sammantha: Find the 3rd term of the sequence, an=1.5(4)n  1. Answered by Penny Nom. 





The nth term of a sequence 
20110701 

From Rachel: I am trying to help my son get ready for our Aims test and I am not much help. The sequence is 2,5,10,17 The question is which equation represents the rule for finding the nth term for this sequence
a. an=n + 1
b. an=2n2
c. an=n2+1
d. an=2n+1 Answered by Penny Nom. 





The nth term 
20110430 

From Samantha: predict the general term, or the nth term, An for the sequence.
1/2,2/3,3/4,4/5,5/6 Answered by Penny Nom. 





The sequence 2,3,5,5,8,7,11 
20110119 

From taylor: number relationship in number sequence 2,3,5,5,8,7,11 Answered by Chris Fisher and Penny Nom. 





What is next in the sequence? 
20110113 

From jodi: what is next in the sequence 1, 1/4, 1/9, 1/16, 1/25 Answered by Penny Nom. 





A geometric progression 
20101215 

From Abeth: find the value of x so that 2(x1), x+3, x will be a geometric progression. Answered by Penny Nom. 





rat sequence 
20100924 

From Vishal: this is known as rat sequence. I want to know the logic pf this :
1,2,4,8,16,77,145 Answered by Chris Fisher. 





The nth term 
20100914 

From Anna: The problem is 2n2. find the nth term. I'm lost as how to even begin Answered by Penny Nom. 





A pattern in a puzzling sequence 
20100709 

From Martha: A1 2 3 B 5 6 7 C 9 10 11 D 13 14 15
USE THIS PATTERN SUGGESTED TO HELP YOU FIND
THE MISSING TERMS IN THE PROBLEM BELOW:
a) H _ _ _ b) R _ _ _
c) _ _ 50 _ d) _ _ _ 63
e) _ @#$ where @ + # + $ = 258 Answered by Tyler Wood. 





The nth term 
20100509 

From Jessica: what is the nth term of 3, 9, 19, 33, 51
please help Answered by Walter Whiteley. 





A geometric progression 
20100430 

From Kalyani: sum of infinite geometric progression is 9 and common ratio is 1/10
then sum up to 8 terms is? Answered by Chris Fisher. 





4 + 10 + · · · + (6n − 2) 
20100421 

From Lan: Find the sum 4 + 10 + · · · + (6n − 2). The answer is 3(n^2) + n. How? Answered by Penny Nom. 





A sequence 
20100413 

From Essence: hello,
I am having trouble doing my math homework. It asks me to write the first five terms of each sequence .I can not figure it out because it is a fraction.
The Problem Is:
{2n+1/2n} Answered by Penny Nom. 





A geometric sequence 
20100413 

From glen: A geometric sequence has a first term of 0.1024, a second term of 0.256,
and a middle term of 156.25. how many terms are there in the whole
sequence?
i know that r=2.5 but i dont know how to find how many terms there are. Answered by Penny Nom. 





1/1+1/2+1/3... 
20100331 

From Mohd: you explained the way of getting the summation of 100 series numbers
but what is the summation of the numbers 1/1+1/2+1/3+1/4+1/5.............................+1/100 Answered by Robert Dawson. 





A geometric sequence 
20100222 

From Kelsey: _, 2, _, _, 250, _
i don't know how to fill in the missing terms Answered by Penny Nom. 





The first five terms of a sequence 
20100214 

From Joanne: Find the first five terms of the sequences with the nth term given as follows.
n^2+3n Answered by Penny Nom. 





A sequence 
20100207 

From Shalev: hi,
i had a job interview yesterday. it had mathematical questions. couldn't solve 1. i m obsessed with it. please find out what the answer is..
it goes like this:
2,4,5,5,8,6,_,_,14,8
thank u very much Answered by Claude Tardif. 





A sequence 
20100127 

From Haku: if there are 8 dots in the first shape, 13 in the second, 19 in the third, and 26 in the fourth, then what is the formula? Answered by Penny Nom. 





A sequence 
20100122 

From brahmaji: 0 7 26 63 _ 215 342 fill the blank? find the missing number Answered by Robert Dawson. 





7 36 14 18 28 9 56 x y 
20091206 

From lisa: what is the sequence of x and y
7 36 14 18 28 9 56 x y Answered by Penny Nom. 





What number comes next? 
20091125 

From Mark: Can someone help and give me the break down of how to solve. 5,3,1,1 Answered by Penny Nom. 





A sequence of letters and numbers 
20091110 

From Maria: What is the last ten letters and numbers in the following series and how do I work it out so I can explain it to an eleven year old.
J1F8M1A0M1J0J1 Answered by Robert Dawson, Claude Tardif and Harley Weston. 





What's the next term? 
20091103 

From bharat: if
1=5
2=25
3=325
4=4325
5=? Answered by Robert Dawson and Penny Nom. 





A sequence 
20091020 

From Alyce: The rule of this sequence is k=1/8n. Find the 8th term of the sequence.
1/8, 1/4, 3/8, 1/2, ...
Thanks! Answered by Penny Nom. 





The next three terms 
20091016 

From Shawn: I'm a parent and don't know how to help my 6th grader solve for this problem.
Name the next tree terms in this sequence and tell the rule used to find each:
1,0,1,0,1,2,3,8,25,..... Answered by Chris Fisher. 





What is the next term? 
20091004 

From julia: patterns
18 46 94 63 52 61 what is the next one? Answered by Penny Nom. 





How many terms are there in this sequence? 
20090928 

From tabby: How many terms are there in this sequence?
5,1,3,...,111 Answered by Penny Nom. 





A sequence 
20090919 

From Oliver: I am struggling to work out the missing terms in the following sequence:
1, 3, _, 7, 11, 18, _ Answered by Chris Fisher. 





A sequence 
20090915 

From Derek: what are the next four numbers in this sequence 1/8, 1/4, 3/8, 1/2... Answered by Penny Nom. 





The nth term of a sequence 
20090911 

From Michael: My son has this question as part of his key stage 3 maths homework
The nth term of a different sequence is n  2/n^2.
We've got to find the first three terms of the sequence. Answered by Claude Tardif. 





Arithmetic Sum & Sequence 
20090901 

From Alice: Find the 24th term of this sequence
6.8,8.0,9.2...
Find the sum of the first 21 terms Answered by Janice Cotcher. 





Sequence problem 
20090818 

From James: I have the equation: t_{n} = (n)(n+1)/2
Which gives the sequence: 1, 3, 6, 10, 15 etc.
However, I'd like to be able to solve for n.
So that a t of 6 would give me the answer of 3, and t of 10 would give me the answer 4 etc. Answered by Stephen La Rocque and Victoria West. 





Finding the Common Difference and Number of Terms of an Arithmetic Sequence 
20090724 

From Juan: In an arithmetic sequence, the first term is 2, the fourth term is 16 and the nth
term is 11,998
A. What is the common difference?
B. What is the value of n. Answered by Janice Cotcher. 





A sequence 
20090711 

From jamie: what is the next number in the sequence and what is the relationship of the numbers? 36,16,20,10,12, _ Answered by Penny Nom. 





Successive differences 
20090618 

From Jonathan: I'm trying to find the next number sequence for this equation: 1 11 35 79 149 251, my problem is that I worked it out and ended up with a single number 17. What am I doing wrong. Thank you for any help. Answered by Robert Dawson and Penny Nom. 





A sequence 
20090526 

From Jay: what is the equation that would give me the next 3 numbers in this progession: 0,1,5,14,20 Answered by Stephen La Rocque. 





A sequence 
20090518 

From Richard: This is my question about sequences.
Write down the nth term of the following sequences.
1/2, 3/4, 9/8, 27/16
Plz help me solve the question! Answered by Penny Nom. 





A number sequence 
20090508 

From alicia: what is the next number 1,2,6,42,1806? is it 1954? Answered by Robert Dawson, Chris Fisher, Penny Nom and Claude Tardif. 





A sequence 
20090313 

From Shelly: Which sequence satisfies the rule n/4? Answered by Stephen La Rocque. 





A sequence 
20090311 

From Vly: 2; 6; 26;126;626 find the nth term Answered by Harley Weston. 





Where do X, Y and Z go? 
20090227 

From Aj: A E F H I K L M N T V W
B C D G J O P Q R S U
where do X, Y and Z go? Answered by Robert Dawson. 





1 3 6 10 15.... 
20090226 

From Allie: 1 3 6 10 15....
i know the pattern is +2 +3 +4 +5 and so on...but i dont know how to write an equation to find the nth term. help! Answered by Robert Dawson and Claude Tardif. 





The sequence 5, 12, 19, 26, ... 
20090204 

From Vickie: Hello,
Here's the question. Ryan wanted to play basketball on a team, He started practicing shooting everyday to improve his skills. The first day he make 5 shots, the second day he made 12 shots, the third day he made 19 shots, and the fourth day he makde 26 shots. If the first day was March 1 and the pattern continues, how many shots will Ryan make on the last day of April and the last day of July? My daughter's answers were 425 for April and 1069 for July. Are these correct and what would be the formula for this question? ? +N=? I don't know please help.
Thank you,
Vickie Answered by Robert Dawson and Penny Nom. 





The sequence 2n!  1 
20090201 

From Penny: I am trying to help my son with this problem. Find the first five terms of the sequence that can be written from the formula A= 2n !1. Answered by Penny Nom. 





Jon's bank account 
20090103 

From Abigail: Hi, i have an exam soon (monday =[ )
in my revison book, it shows two peoples bank accounts and then it says
"write a formula to show the balence of Jon's bank account after n weeks of 2003"
this is the table show
Jon's Bank account
Weeks 
Week 1 
Week 2 
Week 3 
Week 4 
Week 5 
Balance(£) 
970 
1035 
1100 
1165 
1230 
Answered by Penny Nom. 





The middle term of an arithmetic sequence 
20081215 

From Leigh: Find the sum of the first fifteen terms of an arithmetic series if the middle term is 92 Answered by Penny Nom. 





The nth term of a sequence 
20081120 

From kim: Find the next 2 terms of the sequence.
11n+2.5 Answered by Harley Weston. 





The nth term of a sequence 
20081116 

From Robin: How do I solve for the next term in the following sequence, I just don't want the answer...I want how to do it to. x,x 1, x 2
Also, how do I solve for the nth term? I can't understand the explanations I've found. He has numbers subscripted in his equations. Answered by Victoria West. 





1/8, 2/7, 1/2, 4/5, ..., ... 
20081106 

From katie: Inductive reasoning, what 1/8, 2/7, 1/2, 4/5, what would be the next two in th sequence. Answered by Penny Nom. 





A sequence 
20081026 

From Nicole: what is the rule to this sequence 3,6,12,24,48..... Answered by Penny Nom. 





The sequence 49,48,46,43,39... 
20081026 

From Kyle: What number comes next in the series 49,48,46,43,39...? Answered by Stephen La Rocque. 





The sequence 6,1,6,2,6,4,6,8,6, 
20081026 

From Kyle: What number comes next in the series 6,1,6,2,6,4,6,8,6,? Answered by Stephen La Rocque. 





nth term 
20081022 

From jen: what is a nth term and how do i find the nth term of any sequence Answered by Penny Nom. 





The nth term 
20080929 

From shauna: The first five numbers in a sequence are
40, 37 34, 31, 28
Find an expression for the nth number in the sequence. Answered by Penny Nom. 





3,6,10,15,and 21 
20080928 

From jarred: i am currently stumped on a math project that requires me to find out the recursive formula for a sequence of numbers. the numbers in the sequence are 3,6,10,15,and 21. Thank you for your time. Answered by Walter Whiteley. 





Finding the Pattern in a Sequence 
20080916 

From sjp: please could you help me find the nth term for
8 4 0 4 8
and
4 1 4 11 20
Thank you Answered by Janice Cotcher. 





The nth term of a sequence 
20080913 

From lavett: what is the Nth term in the sequence when the sequence is 2,4,8,16... and the term numbers are 1,2,3,4... Answered by Stephen La Rocque. 





0.151515...=15/99 
20080908 

From Emma: This week, my Algebra teacher told us about the pattern between infinitely repeating
decimals and their corresponding fractions.
(ex. .2222222...= 2/9, .151515...=15/99, 456456456...=456/999, etc.)
I was just wondering the reason why this pattern occurs.
Is there a certain element that causes this pattern to occur?
Thanks
Emma Answered by Penny Nom. 





Cost of pencil is rising every year since 7 years ago 
20080806 

From Mari: Cost of pencil is rising every year since 7 years ago. If the cost of
pencil last year was 60 cents which is the sum of the cost from the
last two previous years, what is the cost of the pencil now, the cost
seven years ago. Answered by Penny Nom. 





Does the sequence 1 2 4 8 16 32 etc have a name? 
20080717 

From Richard: Just an idle thought really. Does the simple sequence 1 2 4 8 16 32 etc have a name? Answered by Victoria West. 





1, 2, 4, 8, 16, 32 ... 
20080715 

From eve: I have to find out the fomula for:
1, 2, 4, 8, 16, 32 ... Answered by Penny Nom. 





Geometric sequences 
20080608 

From Rita: A geometric sequence is given. Find the common ratio and write out the first four terms.
(1) {(5)^n}
(2) {(2^n)/(3^(n  1)} Answered by Penny Nom. 





A recursive formula for 9, 18, 36, 27, ... 
20080605 

From Rita: I am having trouble understanding how to write formulas (I should say create formulas) from a given sequence.
It does not matter what sort of sequence it is. The confusion remains.
I have not found a textbook or easy math book that explains this process for the average Joe to grasp.
Here are the two questions:
(1) Write a recursive formula for the sequence
9, 18, 36, 72, ...
(2) Write a recursive formula for the sequence
3, 3(sqrt{3}), 9, 9(sqrt{3}) Answered by Penny Nom. 





33+33+3.........up to infinite terms = ? 
20080425 

From Jatin: 33+33+3.........up to infinite terms = ? Answered by Stephen La Rocque. 





5 9 1 6 10 12 2, where does 3 fit in and why? 
20080322 

From Cassidy: number sequence
5 9 1 6 10 12 2, where does 3 fit in and why? Answered by Claude Tardif. 





4,12,24,40,60,84 
20080318 

From kirsty: Here are the first six terms of a sequence.
4,12,24,40,60,84
Find in terms of n, an expression for the nth term of teh sequence. Answered by Stephen La Rocque. 





The nth term 
20080316 

From ryan: need help figuring nth term for 1, 2, 5, 14, 41...... could you please help Answered by Penny Nom. 





1, 1, 2, 3, 5, 8, 13, ___ ___ ___ 
20080313 

From Karen: What is the rule for the following pattern, and what would come next?
1, 1, 2, 3, 5, 8, 13, ___ ___ ___ Answered by Penny Nom. 





Find the next terms 
20080220 

From Darrin: I was given a number sequence and can't figure out the next terms to this
2,9,20,35,66,91...... Answered by Penny Nom. 





O.T.T.F.F.S.S 
20080125 

From Omar: What is the next letter in the following sequence:
O.T.T.F.F.S.S Answered by Penny Nom. 





1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128 
20080122 

From Neil: Find the next two terms in the following number sequence
1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128
Find a general rule for the nth term of the sequence Answered by Penny Nom. 





Practical applications of sequences 
20080101 

From carl: can you give me examples of different kinds of practical applications of sequences? Answered by Penny Nom. 





O,T,T,F,F,S,S,?,?,? 
20071128 

From Kim: What are the next 3 letters in this sequence?
O,T,T,F,F,S,S,?,?,? Answered by Stephen La Rocque. 





Two sequences 
20071114 

From Kim: Pattern........what comes next?
1,4,9,16,25,_____,____
1,4,9,16,27,40,__________,_______ Answered by Penny Nom and Gabe Potter. 





The sequence 3,12,26,45.... 
20071112 

From Tra: I can seem to find the realtionship in these sequence of numbers, I am looking for the next three. How can I determine that, I have tried everything??!!!
3,12,26,45.... Answered by Penny Nom. 





The nth term 
20071018 

From shannon: Ok , what i am having problems with is the nth term. I get how the numbers come together, but i am having trouble with finding the nth term. Answered by Penny Nom. 





0,1,2,3,6,11,20,37,68... 
20071016 

From Pat: Describe the rule for this pattern:
0,1,2,3,6,11,20,37,68...
Thanks Answered by Penny Nom. 





77,49,36,18,... 
20071011 

From Kim: Find a pattern and predict what comes next in this sequence 77,49,36,18,________________. Answered by Penny Nom. 





A sequence of numbers 
20070930 

From eleanor: can you find the nth term of the sequence ( n starts at three)
1=?
2=?
3= 4
4= 10
5=20
6 = 35
7= 56
i only hand the 3rd 4th 5th 6th and 7th numbers in the sequence
can you please tell me how to find the nth term and what is it :) Answered by Stephen La Rocque and Victoria West. 





The nth term 
20070929 

From zoe: what is the nth term for the following sequence...
5, 2, 1, 4 Answered by Leeanne Boehm. 





Describe the pattern 
20070929 

From Baffled: Given a rule, extend a pattern and describe it in informal mathematical language:
a) 1, 6, 16, 36, _
b) 2, 6, 14, 30, _
c) 1, 8, 22, 50, _
d) 3, 9, 27, _
e) 2, 7, 17, 37, _ Answered by Stephen La Rocque and Penny Nom. 





The nth term 
20070925 

From Bobby: whats the nth term of 2,12,22,32 ? Answered by Penny Nom. 





The sequence 2,4,7,11,16,22 
20070922 

From Simon: I thought i understood how to explain how to work out the nth term on a
sequence of numbers until my son had this sequence to work out 
2,4,7,11,16,22
We have worked out the 2nd differance is +1 but nothing else seems to fit.
Im sure the answer is staring us in the face but cant see the wood for the
trees! Answered by Denis Hanson and Steve La Rocque. 





A fraction sequence 
20070921 

From marissa: i have read the examples you have on fraction sequences, but i am still having
a hard time understanding how to figure this out. for example:
__ 1 2/5 __ 3 __ __ __ __7 Answered by Stephen La Rocque. 





Letter number sequence 
20070921 

From Hope: The challenge problem of the week in 6th grade math is a letter number sequence.
J 1 F 8 M 1 A 0 M 1 J 0 J 1 _ _ _ _ _ _ _ _ _ _
They are to find the next 10 letters and numbers in the line.
They were given a hint : look at the letter sequence by themselves and you should recognize it.
Does it just repeat starting with the F 8 M 1 etc.?
Thank you for your help. Answered by Claude Tardif. 





The nth term 
20070913 

From Rookin: Can you help me find the nth term for this ...
20,17,14,11,8
i'm really confused oh and could you also tell me how you got the answer? Answered by Steve La Rocque, Claude Tardif and Harley Weston. 





What are the next two terms? 
20070911 

From Sassy: I can't figure out what the next two integers in this pattern are 3,9,6,12,9 are. Answered by Stephen la Rocque. 





A sequence of fractions 
20070910 

From mitch: find an expression for T(n), the nth term of the sequence
1/5, 3/8, 5/13, 7/20, 9/29 Answered by Stephen La Rocque. 





The nth term 
20070909 

From Conor: Please can you help me with this question on the subject of the Nth term.
3.5, 5, 6.5, 8, 9.5
5.1, 7.2, 9.3, 11.4... Answered by Penny Nom. 





nth term in this series 
20070907 

From danii: im trying to solve the nth term for this pattern.
1 3 6 10 15 21 28
any help would be appretiated Answered by Stephen la Rocque. 





The next term 
20070907 

From Ariel: Please explain to me why 3^2 is a 9. One calculator give me an answer of positive 9.
WHAT IS THE NEXT TERM IN Each sequence/ What is its term number?
1/2, 2/3, 3/4, 5/6 6/7
1, 1/4, 1/9, 1/16 Answered by Stephen la Rocque. 





A sequence 
20070906 

From aimee: i have the sequence
1,5,14,30,55 and i have been told to use
An squared times Bn times C
and my working should look like this
1 5 14 30 55
4 9 16 25
5 7 9
2 2
But how do i do this Answered by Penny Nom. 





A sequence of fractions 
20070905 

From Arjun: 1/2 3/5 5/8 7/11 need to find the nth term.
I did search the data base & found one for fractions but what I want to know is when calculating nth term for the denominator in the example give in your database how do we get (n1)?
When we deduct the actual term with the one that is in the table give in your example it is more that one. Could you please explain solving the above example? Answered by Penny Nom. 





The first five terms 
20070904 

From JP: Find the first five terms of a sequence with the nth term n^2+2n+1
and 2^n. Answered by Penny Nom. 





2,6,7,21,22,66,67 
20070828 

From EDWIN: this doesnt make any sense to me....... i cant find the pattern...
2,6,7,21,22,66,67 Answered by Leeanne Boehm and Stephen La Rocque. 





The tens digit 
20070821 

From Arul: Hi..
Please help me on this question..
Sequence 2, 7, 22,…after the first three terms, each term is three times the previous term plus 1, a(n+1)=3an + 1. What is the sum of tens digit 33rd and tens digit of the 35 term? Answered by Penny Nom. 





4,18,48,100, __ 
20070807 

From Jeremy: What is the next number in the following sequence?
4,18,48,100, __ Answered by Leeanne Boehm and Stephen La Rocque. 





A sequence of numbers 
20070727 

From Shamik: Question: A sequence of numbers is defined in the following way.
B(1) = 1
B(n) = B(n1) + {Sum of the digits of B(n1)} for n > 1.
B(1) = 1
B(2) = 2
B(3) = 4
B(4) = 8
B(5) = 16
B(6) = 23
B(7) = 28
B(8) = 38
B(9) = 49
::::::::: and so on ...
Is the number 123456789 a term in the given sequence?
Shamik Answered by Claude Tardif. 





What is the 100th term? 
20070615 

From George: I have the sequence
50,120,235,406,644
the 1st difference is 70,115,171,238
the 2nd difference is 45,56,67
the 3rd difference is 11,11
i used the a*n^3+b*n^2+c*n+d rule but the a turns out to be a decimal
because 11/6 is 1.833333333 and so i cant find the formula for the 100th term
term. Answered by Penny Nom. 





How many terms in this sequence? 
20070611 

From Jesse: How do I find how many terms are in the sequence? 51, 48, 45, ...., 75 Answered by Stephen La Rocque and Penny Nom. 





3, 6, 12, 21, 33, 48, 66 
20070502 

From Siew: I need to find the nth term formula for the sequence :
3, 6, 12, 21, 33, 48, 66 Answered by Stephen La Rocque. 





Where will volume 13 go? 
20070412 

From Shawn: A novice librarian shelved a twelvevolume set of encyclopedias in the following order from left to right. Volumes 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and 2. Using her system, where will volume 13 go? Answered by Stephen La Rocque and Penny Nom. 





What are the first 3 terms of this sequence 
20070410 

From kyrie: what are the first 3 terms of this sequence
n2 divided by n squared Answered by Stephen La Rocque. 





4,7,16,43,... 
20070404 

From claire: What is the explicit definition for the sequence 4,7,16,43,...? Answered by Stephen La Rocque and Penny Nom. 





Find the nth term 
20070227 

From Dinky: My teacher has set us a project, but i am having trouble finding the nth term for this. the numbers are: 1, 2, 6, 24, 120 could you please help me? thank you dinky113 Answered by Stephen La Rocque and Penny Nom. 





Arithmetic Series 
20070218 

From Krista: Question The sum of the first 4 terms of an arithmetic series is 8 and the sum of the first 5 terms is 500. Determine the sum of the 3 terms. Answered by Stephen La Rocque. 





What is the index of the term '119' in the sequence 2, 5, 8, 11? 
20070216 

From joey: What is the index of the term '119' in the sequence 2, 5, 8, 11? Answered by Penny Nom. 





The nth term 
20070213 

From Sarah: I am having difficulty in finding the nth term for 7,49,343,2401. Could you please help me in finding the correct answer? Answered by Stephen La Rocque. 





The sum of a sequence 
20070211 

From joey: find the sum of the first 98 terms of the sequence 3, 5, 1, 3, 5, 1, 3, Answered by Penny Nom. 





Find the next 3 terms of the sequence 
20070207 

From rose: find the next 3 terms of the sequence 2,3,9,23,48,87 Answered by Penny Nom. 





5,8,11,14,17 
20070118 

From Mairead: the sequence i was given was 5,8,11,14,17 what is the nth term and what is the 10th term ? Answered by Paul Betts. 





Find the total distance the swing traveled before it stopped. 
20061217 

From Leah: Rebecca's little sister liked for her to push her in the swing at the park. The other day Rebecca pulled the swing back and let it go. She would have kept pushing, but she suddenly saw a friend at the other end of the park. The swing traveled a total distance of 10 feet before heading back the other way. Each swing afterwards was only 80% as long as the previous one. Find the total distance the swing traveled before it stopped. Answered by Penny Nom. 





1, 3, 6, 10... 
20061215 

From Lisa: What is the nth term for the sequence, '1, 3, 6, 10...' and could you say how you got the anwser. Answered by Stephen La Rocque and Penny Nom. 





The nth term 
20061215 

From Lisa: I have worked out that the nth term for 1, 4, 9, 16 is n squared and 3, 5, 7, 9 is 2n  1, so what is the rule for the sequence 1x3, 4x5, 9x7, 16x9? Answered by Penny Nom. 





The nth term 
20061214 

From Hepzibah: what is the definition of nth term and n? Answered by Penny Nom. 





A geometric sequence 
20061128 

From Jillian: Find x so that 2x, x + 5, x  7 are consecutive terms of a geometric sequence. Answered by Stephen La Rocque. 





The Fibonacci sequence 
20061121 

From Ross: Let f0 = 0; f1 = 1,... be the Fibonacci sequence where for all n greater than or equal to 2 fn = fn1 + fn2. Let Q = (1+square root of 5)/2. Show that for all positive n greater than or equal to 0, fn less than or equal to Q^(n1). Answered by Penny Nom. 





On day 1 on which day will 96 students donate food? 
20061119 

From Veydee: during a canned food drive the number of students who donate food doubles each day. If three students donate food on day 1 on which day will 96 students donate food? we have to find the term rule for this pattern Answered by Penny Nom. 





Induction 
20061116 

From John: Find a formula for 1/(1x3)+1/(2x4)+1/(3x5)...+1/(n(n+2)) by examining the values of this expression for small values of n. Use mathematical induction to prove your result. Answered by Penny Nom. 





1,4,9,16,25,36..... 
20061106 

From Teje: i cannot find the next number for this sequence 1,4,9,16,25,36..... could u help please Answered by Stephen La Rocque. 





The sum of 2000 consecutive integers is 1000 
20061029 

From Matias: if the sum of 2000 consecutive integers is 1000, then the sum digits of the greatest of these 2000 integers is? Answered by Penny Nom. 





How many sequences are possible? 
20061028 

From Sam: A fair eightfaced die with faces numbered 1,2,3,4,5,6,7 and 8 is tossed six times and the sequence of numbers is recorded. How many sequences are possible? Answered by Penny Nom. 





A number pattern 
20061002 

From Tim:
The patterns that went in 2s, 4s and 5s we got, but we are stuck on the pattern that doubles. We can't come up with the rule or equation that solves it.
With the first number being the term number and the second being the term, this is the pattern:
11
22
34
48
516
632
764
100128
What is the rule for this?
Answered by Stephen La Rocque and Penny Nom. 





2 5 11 17 23 31 ? 
20060928 

From Bernice: How do you determine the next number in the following sequence: 2 5 11 17 23 31 ? Answered by Penny Nom. 





Find the nth term 
20060913 

From Shakira:
my question is  Find an expression for the nth term of each sequence.
a. 6,15, 28, 45, 66
b, 1/5, 3/8, 5/13, 7/20, 6/29  these are fractions
Answered by Penny Nom. 





5, 3, 2, 1, 1, 0, __, __ 
20060912 

From Sherrie: next two terms in the sequence:
5, 3, 2, 1, 1, 0, __, __ Answered by Stephen La Rocque. 





13 57 91 11 31 51 ?? 
20060615 

From Chastity: im trying to determine the missing number in the sequence
13 57 91 11 31 51 ?? Answered by Claude Tardif, Steve La Rocque and Natasha Glydon. 





What is the sum of the first 100 whole numbers? 
20060531 

From Jo: what is the sum of the first 100 whole numbers? Answered by Natasha Glydon, Paul Betts and Penny Nom. 





The nth term of a sequence 
20060524 

From A student: please could you give me a formula for the following numbers for my teacher
3 8 15 24 35 Answered by Chris Fisher. 





Geometric sequence and basic functions (graphs) 
20060420 

From Marlene: Which of the basic functions is related to the geometric sequence:
Linear, Quadratic, Rational, or Exponential?
Can you give me an example of how it would be used in normal life? Answered by Stephen La Rocque. 





Arithmetic and Geometric Sequences 
20060419 

From Skye: If the 1st, 4th, and 8th terms of an arithmetic sequence are consecutive terms in a geometric sequence, find the common ratio of the geometric sequence. Answered by Stephen La Rocque. 





The product of successive terms in sequences 
20060413 

From Forrest: 1) Find three successive terms in an arithmetic sequence such that their sum is 24 and their product is 440
2) Find three successive terms in a geometric sequence such that their sum is 21 and their product is 216 Answered by Penny Nom. 





Arithmetic Sums 
20060412 

From Angel: (a) In a particular arithmetic sequence, u6 = 344.5 and u20 = 88.3. Find S28.
(b) In a particular arithmetic series, S10 = 495 and S15 = 1005. Express S15 in sigma notation. Answered by Stephen La Rocque. 





Sum of a Geometric Sequence 
20060411 

From Andre: In a particular geometric sequence, U3=3.6 and U10=12.9. Find S16 and S17. Answered by Stephen La Rocque. 





8,_,4,9,1,_,10,3,_,0 
20060308 

From Rachel: I cant figure out this sequence if someone could help me
8,_,4,9,1,_,10,3,_,0 Answered by Claude Tardif. 





2,4,9,6,5,6,____,____,____,... 
20060306 

From Mike: I am having problems figuring out the following sequence:
2,4,9,6,5,6,____,____,____,...
We were able to guess that the pattern simply started to reverse itself,
but I was wondering if there were other possibilities.
Answered by Claude Tardif. 





The nth term 
20060305 

From Umar: my question is what is the nth term for a house of cards 4 stories high if you use the following numbers:
2 7 15 26 Answered by Penny Nom. 





The nth term of a sequence 
20060221 

From Mike: I'm having trouble finding the nth term in an equation, can you help me? Answered by Stephen La Rocque. 





Arithmetic progressions 
20060131 

From A student: 1)the sum to n terms of a particular series is given by S_{n}=17n3n^{2}
a)find an expression for the n term of the series
b)show that the series is an arithmetic progression
2)a particular arithmetic progression has a positive common difference and is such that for any three adjacent terms ,three times the sum of their squares exceeds the square of their sum is 375.Find the common difference
Answered by Penny Nom. 





Finding the nth term in fractions 
20060123 

From Zarina: Each term in this sequence is made by increasing the numerator by 1 and the denominator by 3. here are the first five terms:
1/4, 2/7, 3/10, 4/13, 5/16, ...
(a) write an expression for the nth term: Answered by Penny Nom. 





A sequence of circles and tangents 
20060116 

From Paul: Consider a circle whose center is (2,2) and whose radius is 1, and the
straight line that goes through the origin and that is tangent to this
circle so that the intersection between them is as shown in the attached
picture. With this new point we make a new circle whose radius is half
of the first one, and we calculate the corresponding intersection point
with the same suppositions as in the first case. We repeat the process
to the infinite. Find the distance between the center of the circle in
the infinite and the origin (point (0,0)). Answered by Chris Fisher. 





Find the nth term 
20051214 

From Kevin: How do i find the nth term of 1 4 9 16 25 36 Answered by Penny Nom. 





The stair problem 
20051206 

From Arnold:
My daughter had me help her with some of her college math problems that require finding the pattern. The problem was the stair problem where you can climb either 1 step or 2 steps at a time. How many combinations are there to get to the 10th step. I found the data set that solves the answer to the question, but is there an equation that expresses the answer in terms of n?
1 2 3 4 5 6 7 8 9 10 stair number
1 2 3 5 8 13 21 34 55 89 number of possible combinations
Answered by Harley Weston. 





An Arithmetic sequence 
20051201 

From Aana:
The first term in an arihmetic series is 25 and the 3rd term is 19. Find the number of terms in the series if its is 82.
Here's what I did to find d
a+2d=19; 25+2d= 19 ;1925=2d d=6/2=3
This is where I'm stuck. Can you please provide me with some guidance.
Answered by Penny Nom. 





2, 6, 12, 20, 30, ... 
20051101 

From Rebecca: I have a sequence of I have a sequence of 2, 6, 12, 20, 30, and have no idea how to figure out the nth term please help! Answered by Claude Tardif. 





Find the next 5 terms 
20050924 

From Grant: n+7, 2n0.5, 4n. Find the next 5 terms of each one and explain the sequence in words Answered by Penny Nom. 





Find the first five terms of this sequence? 
20050917 

From Jade: my homework says can you find the first five terms of this sequence?
5n6 i can`t figure it out. Answered by Penny Nom. 





Finding the nth term 
20050912 

From Paul:
Hi , Im having a problem helping my daughter to find the Nth Term in the following sequences.
1/3 1/2 3/5 2/3
and
1 3 6 10
Answered by Penny Nom. 





1,4,9,1,6,2,5,3,6,4,9,6,4,8,1 
20050830 

From Liz: Find the next four numbers to the sequence 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,___,___,___,___. Answered by Penny Nom. 





A geometric sequence 
20050621 

From A student:
The first three terms of a geometric series are 3(q+5), 3(q+3), (q+7) respectively.
Calulate the value of q. Answered by Penny Nom. 





An arithmetic progression 
20041224 

From A student: the 4th and 5th term of an arithmetic progration 47 and 52 respactively find
a)d
b)a1
c)a50 Answered by Penny Nom. 





A sequence 
20041211 

From Amanda: Find the nth term of the following sequence
4, 10, 28, 82 Answered by Penny Nom. 





Geometric sequence 
20041204 

From Lesa: Find a formula for the geometric sequence: (√3  √2), (4  √6), (6√3  2√2), … Answered by Penny Nom. 





Proof by induction 
20041120 

From Vic: Problem: Find the first 4 terms and the nth term of the infinite sequence defined recursively as follows:
a(1) = 3 and a(k+1) = 2a(k) for k > 1.
Note: Quantities in brackets are subscripts
> means 'equal to or greater than'.
Using the recursive formula, the first 4 terms are;
a(1) = 3, a(2) = 6, a(3) = 12, a(4) = 24
The nth term a(n) = 2n1 x 3 (equation 1)
Equation 1 must be proven using mathematical induction. This is where I am having a problem. Answered by Penny Nom. 





A sequence 
20041119 

From Liucy: Find the Nth term:
10 40 90 160 250 Answered by Penny Nom. 





1,3,6,11,18,29,__ 
20040921 

From Guillermo: How do you get to the answer of this sequence
1,3,6,11,18,29,__ Answered by Claude Tardif. 





A challenge 
20040917 

From Lasse: xy
xx
xyx
xxx
xyxx
"x" and "y" each represents a number.
Find out the system to make the next line Answered by Penny Nom. 





1+3+5+...+(2n+1) 
20040910 

From Emma: Prove that 1+3+5+...+(2n+1)= (n+1)^{2} Answered by Penny Nom. 





The nth term 
20040908 

From Alex: What is the nth term?... Like what is it?, How do I find it?, and how exactly is used?... Answered by Penny Nom. 





The series from i=1 to n :ai 
20040818 

From Ken: a.) Explain the difference between
the series from i=1 to n :ai
and the series j=1 to n :aj
b.) Explain the difference between
the series from i=1 to n:ai
and the series from i=1 to n :aj Answered by Penny Nom. 





The sum of 4,0,4..., 156 
20040428 

From Christina: find the requested sum of the arithmetic sequence
4,0,4..., 156 Answered by Penny Nom. 





A geometric sequence 
20040413 

From Michael: In a geometric series, the sum of the 2nd and 3rd terms is 60, and the sum of the 3rd and 4th terms is 240. Find the sum of the first 7 terms. Answered by Penny Nom. 





What is the nth term 
20040407 

From Jason: 1 4 10 20 35 56 84
what is the nth term Answered by Claude Tardif. 





The degree sequence of a graph 
20040331 

From Ali: How can i find out {6,6,5,5,5,3,2}is not the sequence of the points of a simple graph,without drawing it? Answered by Penny Nom. 





What's the next term? 
20040322 

From Garrett:
A friend hit me with these questions and won't tell me the answer nor how... please help? I've racked my brain and did all sorts of formulas, but I can't get it to work out... please...
What's the next number in this series...
5, 12, 17, 29, 46, ?
And this series...
12, 19, 28, 39, 52, 67, ?
and these...
ocoa, boco, oboc, dobo, odob, ?
Answered by Claude Tardif. 





Geometric sequences 
20040203 

From Alan: hello, I am a junior in precalculus. we started working on geometric sequences today, it makes perfect sense on how it works. but why is it called that? if you could send me an answer to why geometric sequences have that name, I would be much appreciative. Answered by Chris Fisher. 





The 4th difference 
20031117 

From Jack: If i had a sequence which was the same at the 4th difference, aka difference
to the 4th, like:
1 5 14 30 56 96
(sequence)
4 9 16 26 40
5 7 10 14
2 3 4
1 1
then what would be the set formulars to find out a, b, c, d, and e
as i know the equation has to be an^{4}+bn^{3}+cn^{2}+dn+e Answered by Penny Nom. 





A project about crosses 
20030610 

From Joel:
I have this project to do about crosses and I can't think of what the answer is for the following questions: What is the area rule of the crosses (the table below will help you)? Cross Number  Area sq cm  1  5  2  13  3  25  4  41  5  61  I also need to know what the formula is for it? Answered by Penny Nom. 





$1/week for week 1 and then double each week 
20030528 

From A student: I AM DOING A PROJECT FOR MATH I AM TRYING TO CREATE A SEQUENCE BASED ON: MAKING A SALARY OF $1/WK FOR THE FIRST WEEK WITH IT DOUBLING EVERY WEEK FOR 52 WEEKS, SO MY SEQUENCE LOOKS LIKE THIS: 1,2,4,8,16,32,64,128,256,512,1024 ETC. THERE WOULD BE 52#'s TOTAL IN MY SEQUENCE.I BELIEVE IT IS CALLED A FINITE SEQUENCE. MY QUESTION IS HOW DO I CREATE A FORMULA/RULE FOR THIS PARTICULAR SEQUENCE? MY GOAL BEING TO FIND THE 52nd TERM IN THE SEQUENCE. Answered by Penny Nom. 





Two sequences that agree in the first 4 terms 
20030526 

From A student: Is it possible to have two formulas that define sequences that agree on the first four terms but not the rest? Answered by Penny Nom. 





One one 
20030422 

From Brad: find the next two rows of numbers?
1
1 1
2 1
1 1 1 2
3 1 1 2
1 1 1 2 1 3
Answered by Leeanne Boehm. 





Chopping trees 
20030419 

From Tamara:
The master needs some of the trees (twenty, to be exact) at the back of his spooky old mansion cleared to make way for a new evil laboratory, so he decides to send some his slaves to do the work for him. He initially sends out four of his men, armed with axes, to chop the trees down. Due to the fact he is very impatient, every ten minutes he sends out another man to help with the work. Assuming that it takes one man 30 minutes to chop down 1/3 of a tree, how long till all twenty trees are chopped down? Answered by Penny Nom. 





A sequence that converges to e 
20030316 

From Dane: Something I noticed fooling around with a calculator about 30 years ago. Considering e = 2.718281828459045.... Using Window's Calculator you will find 1.1^{11} = 2.8531167... 1.01^{101} = 2.731861... 1.001^{1001} = 2.71964085... 1.0001^{10001} = 2.71841774... 1.00001^{100001} = 2.7182954... 1.000001^{1000001}1 = 2.178231875... 1.0000001^{10000001} = 2.178219643... There apears to be a pattern. My conjecture is: 1.'infinite number of zeros'1^{1'infinite number of zeros'1} = e. Answered by Penny Nom. 





Finite differences 
20030210 

From Jenny:
I need to find a formula that will work with any number. I am finding the volume of a 3d cross shape. Here are my results so far:
Term Number 0 1 2 3 4 5
nth term 1 7 25 63 129 231
1rst diff 6 18 38 66 102
2nd diff 12 20 28 36
3rd diff 8 8 8
I can't seem to find a formula that will work with any number. Any help would be much appreciated. Answered by Penny Nom. 





The sum of the first 1000 even integers 
20030206 

From Jill: What is the sum of the first 1000 even integers? Answered by Paul Betts. 





Arithmitic sequence 
20030201 

From A student: I am having problems solving this arithmetic sequence... 1, 5, 10, ___, 50, 1.00, ___, 10.00, ... I believe the answers to be 25 and 5.00 but I can't figure why. Answered by Claude Tardif. 





1+2+3+...+500 
20030131 

From Brian: What is the sum of the numbers from 1 to 500 inclusive? Answered by Paul Betts. 





A geometric sequence 
20021202 

From Wanda: the fifth term of a geometric sequence is 5/16. the common ratio is 1/2. What are the first four terms of the sequence. Answered by Penny Nom. 





What is nth term? 
20021106 

From Joga: What is nth term: First sequence: 2, 4,7,11, 16, nth term Second sequence: 4,10, 28, 82, nth term Answered by Penny Nom. 





Sums of evens 
20020914 

From Rosa: How do I find a geometric way to easily compute sums of consecutive even numbers 2 + 4 + 6 + .... Answered by Leeanne Boehm and Harley Weston. 





8,27,64 . . . 
20020905 

From Mike: We have been trying with no luck all night to complete the following math pattern (next 3 entries) 8,27,64 . . . Any ideas?? Answered by Penny Nom. 





1, 2, 4, 8, 16, 32, etc. 
20020904 

From Ginger: I've been working with finding the nth term for a few weeks, and i can't seem to figure this one out! 1, 2, 4, 8, 16, 32, etc. Answered by Leeanne Boehm. 





What is the next term? 
20020621 

From A student: What is the next term in the sequence: 1, 5, 14, 30..... Answered by Penny Nom. 





Sequences that agree on their first four terms 
20020516 

From Mike: Are there two formulas that define sequences that agree on their first four terms, but differ on the fifth term and all succeeding terms? Answered by Chris Fisher. 





What's the next term? 
20020429 

From A student: Find the nth term for the following: 1) 12, 30, 56, 90, 132 2) 6, 30, 84, 180, 330 3) 8, 15, 24, 35, 48 4) 10, 17, 26, 37, 50 5) 24, 40, 60, 84, 112 6) 24, 60, 120, 336, 504
Please show the FULL working out. Answered by Penny Nom. 





A sequence 
20020307 

From Caroline: hi, here is the problem,
1 11 21 1211 111221 _ _ 2_ _ _ we can't get the sequence of the last line ,with the 3rd number being 2,thanks Answered by Walter Whiteley. 





1,4,27,____,_____46656 
20020221 

From Brenda: 1,4,27,____,_____46656..... please find the fourth and fifth numbers in this sequence. Answered by Penny Nom. 





Successive differences 
20020120 

From Linsey: what is the rule for working out the formula for a sequence with three lines of difference? eg.
1, 3, 7, 15, 29
1st line differences: 2, 4, 8, 14
2nd line differences: 2, 4, 6
3rd line differences: 2, 2 Answered by Penny Nom. 





My salary is doubled everyday for 30 days 
20020117 

From Kanishk: I recieve 1 penny the 1st day, 2 pennies the 2nd day, and my salary is doubled everyday for 30 days. How much money will I have by the end of the 30 day time period? (Is there a way of solving this problem without a chart?) Answered by Penny Nom. 





A sequence 
20020116 

From Chris: I have spent two days trying to determine the pattern to the following set of numbers: 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,____. I need the next four numbers to the sequence. Answered by Claude Tardif. 





A sequence of number pairs 
20020110 

From Terry: Three is the first number of a pair, and 8 is the second.
a. If 50 is the first number, what is the second number? b. If 200 is the first number, what is the second number? c. If 89 is the second number, what is the first number? d. If a number n is the first number, what is the second number?
38 411 514 617 ____ ____ ____ 1029 ____ ____ ____
Answered by Peny Nom. 





3, 6, 10, 15, 21 
20011129 

From Patrick: we are trying to find the expression to solve for the nth term in the pattern 3, 6, 10, 15, 21 Answered by Denis Hanson. 





Number sequences 
20011117 

From Stephanie: My name is Stephanie. My grade 7 math class is studying number sequences and, to me, they make almost no sense at all. Here I wrote down 2 of the many problems I have for homework and was wondering if you could explain them to me (I have to find the next 3 numbers in each sequence.) It would be a big help! 10, 14, 18, 22, _, _, _. 12, 21, 39, 75, _, _, _. Answered by Penny Nom. 





2=the square root of (2 + the square root of (2 + the square root of (2 +...))) 
20011105 

From Cynthia: justify algebreically, that: 2=the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + and so on, ....... Answered by Penny Nom. 





1+2+3+...+1000 
20011001 

From Louise: Find a quick way to add all Intergers (whole Numbers) between 1 and 1000? Answered by Walter Whiteley. 





Find the pattern 
20010926 

From A parent: MY SON HAD ON A WORKSHEET WHAT I HAVE LISTED BELOW, BUT WE CAN'T SEEM TO FIND THE PATTERN. MOST THE TIME WE CAN, BUT THIS ONE IS DIFFERENT. 6,___, 9,____,____,_____,_____,_____ Answered by Caude Tardif. 





Four sequences 
20010924 

From Nicole: I have a few questions I couldn't figure it out. So any help will be great to find the next three numbers or letters. Here's the patters...  DEGHNORY, EHILMU, HIILMTU, BEILLMRUY,...
 50, 33, 25, 20, 16, 14, 12,...
 1777, 1795, 1818, 1819, 1820, 1822, 1836, 1837..
 A,H,I,M,O,T,...
Answered by Chris Fisher and Penny Nom. 





Arithmetic sequences 
20010910 

From Rachel: I can't seem to figure out a problem that deals with arithmetic sequencing. This is the question: The 5th term in an arithmetic sequence is 1/2, and the 20th term is 7/8. Find the first three terms of the sequence. I attempted this problem with the formula: An = a + (n1)d (where the n represents the nth term, a is the first term, and d represents the common difference) I keep getting 9.5 for the first number, and then 3/120 as the common difference between the numbers. But as I have figured it, the sequence is getting greater and greater, and my data does not go with the terms given. Answered by Penny Nom. 





A sequence 
20010825 

From Sharon: 1 11 21 1211 111221 312211 1311221 1113213211 31131211131221 13211311123113112211 What would be the next sequence of numbers? my name is sharon i work in customer service and a friend asked me to solve this. Answered by Walter Whiteley. 





A sequence defined recursively 
20010501 

From A student: A sequence s is defined recursively as follows: s_{0}=1 s_{1}=2 s_{k}=2s_{k2} for all integers  Compute s2,s3,s4... to guess an explicit formula for the sequence sk. Answered by Penny Nom. 





A sequence of even terms 
20010429 

From A student: A sequence c is defined recursively as follows: c0 = 2 c1 = 4 c2 = 6 ck= 5ck3 for all integers Prove that cn is even for all integers. Answered by Leeanne Boehm and Penny Nom. 





Geometric and arithmetic sequences 
20010126 

From Garry: what are the equations for geometric and arithmetic sequences? also, what are the equations for finding the sums of those series? Answered by Leeanne Boehm and Penny Nom. 





0,2,3,6,7,1,9,4,5,8 
20010123 

From Tami: What is the sequence of the numbers 0,2,3,6,7,1,9,4,5,8 Answered by Claude Tardif. 





Some terms in a sequence 
20010115 

From jamie: Please help as soon as possible! i am stuck with some terms in a sequence. the terms are 1st term=1, 2nd term=10, 3rd term=35, 4th term=84, 5th term=165, 6th term=286. can anyone tell me the formula for the nth term? n is term number Answered by Sukanta Pati. 





Find the rule 
20001027 

From Kelsa and Linda: Find the rule: It had 13 in a circle then 2 blank circles then 31 in a circle then two more blank circles. Could you please help us. Answered by Penny Nom. 





A sequence question 
20001023 

From Chell: I have the following sequence: 4 16 37 58 89 145 42 20 I have no clue how to arrive at an answer. I've checked to see if it can be defined as an arithmetic or geometric series, and it can't. I've looked for primes and noticed that 37 and 89 are the only primes ... but from there I've lost. Nothing I've tried seems to work, so please help! Thanks a million!!!! Answered by Chris Fisher. 





7     77 
20000913 

From Peter: Does anyone know how to solve the following: 7 _ _ _ _ 77 ? I have to find the missing values. Answered by Chris Fisher and Walter Whiteley. 





The sum of the squares of 13 consecutive positive integers 
20000825 

From Wallace: Prove that it is not possible to have the sum of the squares of 13 consecutive positive integers be a square. Answered by Harley Weston. 





Covering 1, 1/2, 1/3,... 
20000822 

From Wallace: Consider the points 1, 1/2, 1/3, ... on the real number line. You are given five small bars, all of length p, which are to be placed on the number line such that all points will be covered. What is the minimum value of p that will allow you to do this? Answered by Penny Nom. 





Patterning and Sequencing 
20000705 

From Michael Jellis: What would be the next two terms? 1.0,0.5,0.6,0.75,0.8,___,____ please explain!!! I am completely baffled and need all the help I can get! Answered by Claude Tardif. 





A sequence 
20000616 

From Claire Hall: Can you find the formula for the pattern 4,12,24,40,60 Answered by AClaude Tardif. 





The number of seats in an auditorium 
20000516 

From David Evaska: There are 10 students in the first row of seats in an auditorium 12 in the second 14 in the third and 2 additional in each seat. The total number of rows is 40. I know the answer is 1960 can you please show me the formula step by step. Answered by Penny Nom. 





Looking for a pattern 
20000508 

From Laura: Yesterday, me teacher stumped me with a question. He talked to us about square units. He told us an area of 1 square unit produces 1 shape, an area of 2 sq.units produces 1 shape, an area of 3 sq.units produces 2 different shapes, an area of four square units produces 5 different shapes, and an area od five sq.units produces 12 different shapes. He left us there. He said we had to find how many different shapes an area of 1 sq. unit produces through how many different shapes an area of 15 sq.units produces. He said we could complete this "chart" by finding an equation. But, I can't find the equation. I think it may be a quadratic of some sort. My teacher told us to use the area(in sq.units) as X and the # of different shapes produced as Y. Now, what really is stumping me is I would have to have an equation so when X is Y, Y is 1 and when X is 2, Y is 1. I have also tried to see if I can complete a patter or something. The pattern I saw was 1,1,2,5,12. I can't make much sense of that pattern. Answered by Penny Nom. 





Geometric sequences 
20000411 

From Jodie: I am in a grade ten principles class and was taught how to do geometric sequences and series but no one in my class understood what we were taught. Our teacher is one of few to use the new curriculum which used to be the grade twelve curriculum. Could you please explain to me how to do geometric sequences and how to find the different terms and sums. Thank you very much! Answered by Harley Weston. 





Completing a sequence 
20000317 

From David Grimmer: Complete the following sequence so that, after the first two terms, each successive term is the average of all the preceding terms. 20__ __ 28 __ __ Answered by Penny Nom. 





What's the next term? 
20000229 

From Meredith O'Neill: At this point, the whole family wants to know the answer. if possible an explanation. thanks a sequence ? 16,37,58,89,145 ?? Answered by Chris Fisher. 





Number sequences 
19991111 

From Justin Schessler: I CAN NOT figure out this sequence or how we continue this sequence... 3,2,6,5,15,14,___,___,___ Answered by Chris Fisher and Harley Weston. 





Where three sequences meet. 
19990306 

From Ali: My name is Ali and I am in the 5th grade. I have a math question: What is the least positive integer meeting each of the following conditions:  Dividing by 7 gives a remainder of 4
 Dividing by 8 gives a remainder of 5
 Dividing by 9 gives a remainder of 6
Help! Answered by Denis Hanson. 





Finding a rule for a sequence 
19990217 

From Lindsey Masters: I'm doing a maths investigation and i have a sequence which goes: 13,16,25,32,45,56,73. Our teacher told us we have to find a rule by looking at the differences of the terms until we find a constant. The first differences are: 3,9,7,13,11,17. The differences of these are: ...... Please could you tell me how to work it out so that I could work out the rules of similar sequences. Answered by Penny Nom. 





What's the next term? 
19981112 

From Ilia: What the formula and explonation for formula for next patterns: 1) 1, 4, 10, 20, 35, 56, 84,... 2) 0, 6, 30, 90, 210, 420,... Thanks! Answered by Penny Nom. 





Sequences and series 
19980527 

From Michael Le Francois: The sum of the first ten terms of an arithmetic series is 100 and the first term is 1. Find the 10th term. The common ratio in a certain geometric sequence is r=0.2 and the sum of the first four terms is 1248 find the first term. Answered by Penny Nom. 





Pay Phone Problem 
19980226 

From Shameq: Hi, I've been given a problem that I'm having some trouble with. I'd really appreciate any help. Here's the question (it's called the Pay Phone Problem) A pay phone will take only 10p, 20p, 50p, and £1 coins"(It's British). A woman has plenty of 10p and 20p coins. She has no other coins. She can put the coins into the pay phone in any order. INVESTIGATE the number of different ways, she could put the 10p and 20p coins into the pay phone. Answered by Penny Nom. 


