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 Topic: sequence
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An arithmetic sequence 2020-04-04
From ally:
-10 ... last term 35 common difference is 3
(a) find the number of term in the sequence.
i have lost the formula.

What are the next three terms? 2019-06-18
From Shriya:
-6, -2 , 2, 6,10 what are the next three terms?
An arithmetic sequence 2019-02-23
From Dalal:
If x+1 and -x+17 are the second and sixth term of a sequence with a common difference of 5, what's the value of x.
An arithmetic sequence 2019-01-31
From sara:
if the 6th term of an arithmetic sequence is 8 and the 11th term is -2, what is the first term?
The number of terms in an arithmetic sequence 2018-06-15
From Don:
how many terms in arithmetic sequence are there if the first term and the last term are 3&59 respectively in common difference is 4?
Gauss' Addition of whole numbers. 2018-04-30
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?
A puzzling sequence 2017-12-19
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.

An arithmetic sequence 2017-11-30
From yo:
x; 2x+1; 11 are three consecutive terms of an arithmetic sequence.calculate x
An alphabetic sequence 2017-09-17
From malik:
find the letter of the following series....?

ZOTTFFSSE-

An arithmetic sequence 2017-07-17
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

Successive Differences 2017-04-06
From Twaha:
Please find the equation of the sequence 1 2 4 7 11 16 22
A pattern rule for a sequence 2016-10-28
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.

Two sequences 2016-08-20
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)
The sequence 13 17 23 27 33 37 2016-07-29
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.

Which term of this sequence has value 8? 2016-07-20
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 + (n-1)d. In this series a = -2

A geometric progression 2016-03-03
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
Which term of the series 2+7+12+...is 152? 2016-02-01
From francis:
whice term of the series 2+7+12+...is 152?
A sequence 2016-01-05
From Mia:
the next three terms in each sequence. 0.4, 0.54, 0.68, 0.82,
The sequence 1,2,4,7,11,16... 2015-10-15
From HEMANT:
what is the next term in the sequence : 1,2,4,7,11,16,?
The nth term 2015-07-04
From ujjal:
What is the nth term in the order 6,8,10....
A geometric sequence 2015-04-19
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
Some non-decreasing sequences 2015-04-13
From Sky:
Hi I'm a Student and i'll try my best to state the problem perfectly.

The number of non-decreasing 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}]

1,4,9,61,52,___ 2015-01-21
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.
A sequence 2015-01-13
From cyaz:
write a rule for each sequence then find next 3 terms for 7/8, 3 1/8, 5 3/8
Find the nth term 2014-10-26
From Kenneth:
According to the pattern of the following sequence. Find it's nth term: 3,9,27,81,243,..........
The sum of the first 50 terms of an arithmetic progression 2014-07-26
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

9,-4,6,-8,3,... 2014-03-31
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.

An arithmetic sequence 2014-03-20
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.
A sequence 2014-02-10
From Joshua:
hello..the question I have today is... A sequence... 1,5,14,30,55,91 find the general terms.
A sequence 2014-01-30
From joshua:
hi...really struggle with one question that the teacher gave us...
The sequence is 1,2,1,5,8,1,11,___,___

An arithmetic sequence 2014-01-06
From paris:
find the twenty-fifth term of an arithmetic sequence whose first term is 12 and whose common difference is -6
Find the next 3 terms of the sequence 2013-12-19
From Lanelyn:
Find the next 3 terms of the sequence 2,3,9,23,48,87,__,__,__
The sum of all whole numbers from 1 to X 2013-09-06
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
A sequence or a series? 2013-09-05
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

A geometric sequence 2013-07-16
From Relebohile:
Find the n^th term of 3,6,9,12,24,48...
Write a rule for the sequence 2013-02-20
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: _______________
The nth term of a sequence 2012-10-19
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?

An arithmetic progression 2012-08-22
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.
A cylinder is to be filled with peas. 2012-06-12
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?"

A geometric sequence 2012-06-10
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 forty-five. What is the first term of the sequence?
The nth term 2012-05-05
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,

A geometric sequence 2012-02-24
From Camille:
Find x if the sequence 5,10,x+2 is geometric.
A tree growth modelled by a geometric series 2012-02-08
From Steph:
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

Three consecutive terms of an arithmetic sequence 2011-10-30
From Juliette:
Find X when x, 1/2x + 7, 3x -1 are consecutive terms of an arithmetic sequence.
A sequence 2011-08-14
From intesar:
how do i figure this out 0,1/6,2/9,3/12
The third term of a sequence 2011-08-13
From sammantha:
Find the 3rd term of the sequence, an=1.5(4)n - 1.
The nth term of a sequence 2011-07-01
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

The nth term 2011-04-30
From Samantha:
predict the general term, or the nth term, An for the sequence.
1/2,2/3,3/4,4/5,5/6

The sequence 2,3,5,5,8,7,11 2011-01-19
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? 2011-01-13
From jodi:
what is next in the sequence 1, 1/4, 1/9, 1/16, 1/25
A geometric progression 2010-12-15
From Abeth:
find the value of x so that 2(x-1), x+3, x will be a geometric progression.
rat sequence 2010-09-24
From Vishal:
this is known as rat sequence. I want to know the logic pf this :-

1,2,4,8,16,77,145

The nth term 2010-09-14
From Anna:
The problem is 2n-2. find the nth term. I'm lost as how to even begin
A pattern in a puzzling sequence 2010-07-09
From Martha:
A1 2 3 B 5 6 7 C 9 10 11 D 13 14 15

THE MISSING TERMS IN THE PROBLEM BELOW:
a) H _ _ _ b) R _ _ _
c) _ _ 50 _ d) _ _ _ 63
e) _ @#\$ where @ + # + \$ = 258

The nth term 2010-05-09
From Jessica:
what is the nth term of 3, 9, 19, 33, 51

A geometric progression 2010-04-30
From Kalyani:
sum of infinite geometric progression is 9 and common ratio is 1/10 then sum up to 8 terms is?
4 + 10 + · · · + (6n − 2) 2010-04-21
From Lan:
Find the sum 4 + 10 + · · · + (6n − 2). The answer is 3(n^2) + n. How?
A sequence 2010-04-13
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}

A geometric sequence 2010-04-13
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.
1/1+1/2+1/3... 2010-03-31
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
A geometric sequence 2010-02-22
From Kelsey:
_, 2, _, _, 250, _

i don't know how to fill in the missing terms

The first five terms of a sequence 2010-02-14
From Joanne:
Find the first five terms of the sequences with the nth term given as follows. n^2+3n
A sequence 2010-02-07
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

A sequence 2010-01-27
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?
A sequence 2010-01-22
From brahmaji:
0 7 26 63 _ 215 342 fill the blank? find the missing number
7 36 14 18 28 9 56 x y 2009-12-06
From lisa:
what is the sequence of x and y
7 36 14 18 28 9 56 x y

What number comes next? 2009-11-25
From Mark:
Can someone help and give me the break down of how to solve. 5,3,1,-1
A sequence of letters and numbers 2009-11-10
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? 2009-11-03
From bharat:
if
1=5
2=25
3=325
4=4325
5=?

Answered by Robert Dawson and Penny Nom.
A sequence 2009-10-20
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!

The next three terms 2009-10-16
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,.....

What is the next term? 2009-10-04
From julia:
patterns 18 46 94 63 52 61 what is the next one?
How many terms are there in this sequence? 2009-09-28
From tabby:
How many terms are there in this sequence?
5,1,-3,...,-111

A sequence 2009-09-19
From Oliver:
I am struggling to work out the missing terms in the following sequence:

1, 3, _, 7, 11, 18, _

A sequence 2009-09-15
From Derek:
what are the next four numbers in this sequence 1/8, 1/4, 3/8, 1/2...
The nth term of a sequence 2009-09-11
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.

Arithmetic Sum & Sequence 2009-09-01
From Alice:
Find the 24th term of this sequence 6.8,8.0,9.2... Find the sum of the first 21 terms
Sequence problem 2009-08-18
From James:
I have the equation: tn = (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 2009-07-24
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.
A sequence 2009-07-11
From jamie:
what is the next number in the sequence and what is the relationship of the numbers? 36,16,20,10,12, _
Successive differences 2009-06-18
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 2009-05-26
From Jay:
what is the equation that would give me the next 3 numbers in this progession: 0,1,5,14,20
A sequence 2009-05-18
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!

A number sequence 2009-05-08
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 2009-03-13
From Shelly:
Which sequence satisfies the rule n/4?
A sequence 2009-03-11
From Vly:
2; 6; 26;126;626 find the nth term
Where do X, Y and Z go? 2009-02-27
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?

1 3 6 10 15.... 2009-02-26
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, ... 2009-02-04
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 2009-02-01
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.
Jon's bank account 2009-01-03
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 Balance(£) Week 1 Week 2 Week 3 Week 4 Week 5 970 1035 1100 1165 1230

The middle term of an arithmetic sequence 2008-12-15
From Leigh:
Find the sum of the first fifteen terms of an arithmetic series if the middle term is 92
The nth term of a sequence 2008-11-20
From kim:
Find the next 2 terms of the sequence.
11n+2.5

The nth term of a sequence 2008-11-16
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.

1/8, 2/7, 1/2, 4/5, ..., ... 2008-11-06
From katie:
Inductive reasoning, what 1/8, 2/7, 1/2, 4/5, what would be the next two in th sequence.
A sequence 2008-10-26
From Nicole:
what is the rule to this sequence 3,6,12,24,48.....
The sequence 49,48,46,43,39... 2008-10-26
From Kyle:
What number comes next in the series 49,48,46,43,39...?
The sequence 6,1,6,2,6,4,6,8,6, 2008-10-26
From Kyle:
What number comes next in the series 6,1,6,2,6,4,6,8,6,?
nth term 2008-10-22
From jen:
what is a nth term and how do i find the nth term of any sequence
The nth term 2008-09-29
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.

3,6,10,15,and 21 2008-09-28
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.
Finding the Pattern in a Sequence 2008-09-16
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
The nth term of a sequence 2008-09-13
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...
0.151515...=15/99 2008-09-08
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

Cost of pencil is rising every year since 7 years ago 2008-08-06
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.
Does the sequence 1 2 4 8 16 32 etc have a name? 2008-07-17
From Richard:
Just an idle thought really. Does the simple sequence 1 2 4 8 16 32 etc have a name?
1, 2, 4, 8, 16, 32 ... 2008-07-15
From eve:
I have to find out the fomula for:

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

Geometric sequences 2008-06-08
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)}

A recursive formula for 9, -18, 36, -27, ... 2008-06-05
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})

3-3+3-3+3.........up to infinite terms = ? 2008-04-25
From Jatin:
3-3+3-3+3.........up to infinite terms = ?
5 9 1 6 10 12 2, where does 3 fit in and why? 2008-03-22
From Cassidy:
number sequence

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

4,12,24,40,60,84 2008-03-18
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.

The nth term 2008-03-16
From ryan:
1, 1, 2, 3, 5, 8, 13, ___ ___ ___ 2008-03-13
From Karen:
What is the rule for the following pattern, and what would come next?

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

Find the next terms 2008-02-20
From Darrin:
I was given a number sequence and can't figure out the next terms to this

2,9,20,35,66,91......

O.T.T.F.F.S.S 2008-01-25
From Omar:
What is the next letter in the following sequence:

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

1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128 2008-01-22
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

Practical applications of sequences 2008-01-01
From carl:
can you give me examples of different kinds of practical applications of sequences?
O,T,T,F,F,S,S,?,?,? 2007-11-28
From Kim:
What are the next 3 letters in this sequence?

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

Two sequences 2007-11-14
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.... 2007-11-12
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....

The nth term 2007-10-18
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.
0,1,2,3,6,11,20,37,68... 2007-10-16
From Pat:
Describe the rule for this pattern: 0,1,2,3,6,11,20,37,68... Thanks
77,49,36,18,... 2007-10-11
From Kim:
Find a pattern and predict what comes next in this sequence 77,49,36,18,________________.
A sequence of numbers 2007-09-30
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 2007-09-29
From zoe:
what is the nth term for the following sequence...
5, 2, -1, -4

Describe the pattern 2007-09-29
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 2007-09-25
From Bobby:
whats the nth term of 2,12,22,32 ?
The sequence 2,4,7,11,16,22 2007-09-22
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 2007-09-21
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

Letter number sequence 2007-09-21
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.
The nth term 2007-09-13
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? 2007-09-11
From Sassy:
I can't figure out what the next two integers in this pattern are 3,9,6,12,9 are.
A sequence of fractions 2007-09-10
From mitch:
find an expression for T(n), the nth term of the sequence
1/5, 3/8, 5/13, 7/20, 9/29

The nth term 2007-09-09
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...

nth term in this series 2007-09-07
From danii:
im trying to solve the nth term for this pattern.

1 3 6 10 15 21 28

any help would be appretiated

The next term 2007-09-07
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

A sequence 2007-09-06
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

A sequence of fractions 2007-09-05
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 (n-1)? 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?

The first five terms 2007-09-04
From JP:
Find the first five terms of a sequence with the nth term n^2+2n+1 and 2^n.
2,6,7,21,22,66,67 2007-08-28
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 2007-08-21
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?
4,18,48,100, __ 2007-08-07
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 2007-07-27
From Shamik:
Question: A sequence of numbers is defined in the following way.
B(1) = 1
B(n) = B(n-1) + {Sum of the digits of B(n-1)} 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

What is the 100th term? 2007-06-15
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.

How many terms in this sequence? 2007-06-11
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 2007-05-02
From Siew:
I need to find the nth term formula for the sequence :

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

Where will volume 13 go? 2007-04-12
From Shawn:
A novice librarian shelved a twelve-volume 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 2007-04-10
From kyrie:
what are the first 3 terms of this sequence n-2 divided by n squared
4,7,16,43,... 2007-04-04
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 2007-02-27
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 2007-02-18
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.
What is the index of the term '119' in the sequence 2, 5, 8, 11? 2007-02-16
From joey:
What is the index of the term '119' in the sequence 2, 5, 8, 11?
The nth term 2007-02-13
From Sarah:
The sum of a sequence 2007-02-11
From joey:
find the sum of the first 98 terms of the sequence 3, 5, 1, 3, 5, 1, 3,
Find the next 3 terms of the sequence 2007-02-07
From rose:
find the next 3 terms of the sequence 2,3,9,23,48,87
5,8,11,14,17 2007-01-18
the sequence i was given was 5,8,11,14,17 what is the nth term and what is the 10th term ?
Find the total distance the swing traveled before it stopped. 2006-12-17
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.
1, 3, 6, 10... 2006-12-15
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 2006-12-15
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?
The nth term 2006-12-14
From Hepzibah:
what is the definition of nth term and n?
A geometric sequence 2006-11-28
From Jillian:
Find x so that 2x, x + 5, x - 7 are consecutive terms of a geometric sequence.
The Fibonacci sequence 2006-11-21
From Ross:
Let f0 = 0; f1 = 1,... be the Fibonacci sequence where for all n greater than or equal to 2 fn = fn-1 + fn-2. 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^(n-1).
On day 1 on which day will 96 students donate food? 2006-11-19
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
Induction 2006-11-16
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.

1,4,9,16,25,36..... 2006-11-06
From Teje:
i cannot find the next number for this sequence 1,4,9,16,25,36..... could u help please
The sum of 2000 consecutive integers is 1000 2006-10-29
From Matias:
if the sum of 2000 consecutive integers is 1000, then the sum digits of the greatest of these 2000 integers is?
How many sequences are possible? 2006-10-28
From Sam:
A fair eight-faced 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?
A number pattern 2006-10-02
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:

1-1
2-2
3-4
4-8
5-16
6-32
7-64
100-128

What is the rule for this?

Answered by Stephen La Rocque and Penny Nom.
2 5 11 17 23 31 ? 2006-09-28
From Bernice:
How do you determine the next number in the following sequence:
2 5 11 17 23 31 ?

Find the nth term 2006-09-13
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

-5, 3, -2, 1, -1, 0, __, __ 2006-09-12
From Sherrie:
next two terms in the sequence: -5, 3, -2, 1, -1, 0, __, __
13 57 91 11 31 51 ?? 2006-06-15
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? 2006-05-31
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 2006-05-24
From A student:
please could you give me a formula for the following numbers for my teacher 3 8 15 24 35
Geometric sequence and basic functions (graphs) 2006-04-20
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?
Arithmetic and Geometric Sequences 2006-04-19
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.
The product of successive terms in sequences 2006-04-13
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
Arithmetic Sums 2006-04-12
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.
Sum of a Geometric Sequence 2006-04-11
From Andre:
In a particular geometric sequence, U3=-3.6 and U10=12.9. Find S16 and S17.
8,_,4,9,1,_,10,3,_,0 2006-03-08
From Rachel:
I cant figure out this sequence if someone could help me 8,_,4,9,1,_,10,3,_,0
2,4,9,6,5,6,____,____,____,... 2006-03-06
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.

The nth term 2006-03-05
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

The nth term of a sequence 2006-02-21
From Mike:
I'm having trouble finding the nth term in an equation, can you help me?
Arithmetic progressions 2006-01-31
From A student:
1)the sum to n terms of a particular series is given by Sn=17n-3n2

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

Finding the nth term in fractions 2006-01-23
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:

A sequence of circles and tangents 2006-01-16
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)).
Find the nth term 2005-12-14
From Kevin:
How do i find the nth term of 1 4 9 16 25 36
The stair problem 2005-12-06
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

An Arithmetic sequence 2005-12-01
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 ;19-25=2d d=-6/2=-3

This is where I'm stuck. Can you please provide me with some guidance.

2, 6, 12, 20, 30, ... 2005-11-01
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!
Find the next 5 terms 2005-09-24
From Grant:
n+7, 2n-0.5, 4n. Find the next 5 terms of each one and explain the sequence in words
Find the first five terms of this sequence? 2005-09-17
my homework says can you find the first five terms of this sequence? 5n-6 i can`t figure it out.
Finding the nth term 2005-09-12
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

1,4,9,1,6,2,5,3,6,4,9,6,4,8,1 2005-08-30
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,___,___,___,___.
A geometric sequence 2005-06-21
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.

An arithmetic progression 2004-12-24
From A student:
the 4th and 5th term of an arithmetic progration 47 and 52 respactively find
a)d
b)a1
c)a50

A sequence 2004-12-11
From Amanda:
Find the nth term of the following sequence

4, 10, 28, 82

Geometric sequence 2004-12-04
From Lesa:
Find a formula for the geometric sequence: (√3 - √2), (4 - √6), (6√3 - 2√2), …
Proof by induction 2004-11-20
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) = 2n-1 x 3 (equation 1)

Equation 1 must be proven using mathematical induction. This is where I am having a problem.

A sequence 2004-11-19
From Liucy:
Find the Nth term: 10 40 90 160 250
1,3,6,11,18,29,__ 2004-09-21
From Guillermo:
How do you get to the answer of this sequence 1,3,6,11,18,29,__
A challenge 2004-09-17
From Lasse:
xy
xx
xyx
xxx
xyxx

"x" and "y" each represents a number. Find out the system to make the next line

1+3+5+...+(2n+1) 2004-09-10
From Emma:
Prove that 1+3+5+...+(2n+1)= (n+1)2
The nth term 2004-09-08
From Alex:
What is the nth term?... Like what is it?, How do I find it?, and how exactly is used?...
The series from i=1 to n :ai 2004-08-18
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

The sum of 4,0,-4..., -156 2004-04-28
From Christina:
find the requested sum of the arithmetic sequence

4,0,-4..., -156

A geometric sequence 2004-04-13
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.
What is the nth term 2004-04-07
From Jason:
1 4 10 20 35 56 84
what is the nth term

The degree sequence of a graph 2004-03-31
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?
What's the next term? 2004-03-22
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, ?

Geometric sequences 2004-02-03
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.
The 4th difference 2003-11-17
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 an4+bn3+cn2+dn+e

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 NumberArea sq cm
15
213
325
441
561

I also need to know what the formula is for it?

\$1/week for week 1 and then double each week 2003-05-28
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.
Two sequences that agree in the first 4 terms 2003-05-26
From A student:
Is it possible to have two formulas that define sequences that agree on the first four terms but not the rest?
One one 2003-04-22
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
```

Chopping trees 2003-04-19
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?

A sequence that converges to e 2003-03-16
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

1.111 = 2.8531167...
1.01101 = 2.731861...
1.0011001 = 2.71964085...
1.000110001 = 2.71841774...
1.00001100001 = 2.7182954...
1.00000110000011 = 2.178231875...
1.000000110000001 = 2.178219643...

There apears to be a pattern. My conjecture is:

1.'infinite number of zeros'11'infinite number of zeros'1 = e.

Finite differences 2003-02-10
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.

The sum of the first 1000 even integers 2003-02-06
From Jill:
What is the sum of the first 1000 even integers?
Arithmitic sequence 2003-02-01
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.
1+2+3+...+500 2003-01-31
From Brian:
What is the sum of the numbers from 1 to 500 inclusive?
A geometric sequence 2002-12-02
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.
What is nth term? 2002-11-06
From Joga:
What is nth term:

First sequence:
2, 4,7,11, 16, nth term

Second sequence:
4,10, 28, 82, nth term

Sums of evens 2002-09-14
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 . . . 2002-09-05
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??
1, 2, 4, 8, 16, 32, etc. 2002-09-04
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.

What is the next term? 2002-06-21
From A student:
What is the next term in the sequence:

1, 5, 14, 30.....

Sequences that agree on their first four terms 2002-05-16
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?
What's the next term? 2002-04-29
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.

A sequence 2002-03-07
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

1,4,27,____,_____46656 2002-02-21
From Brenda:
1,4,27,____,_____46656..... please find the fourth and fifth numbers in this sequence.
Successive differences 2002-01-20
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 ```

My salary is doubled everyday for 30 days 2002-01-17
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?)
A sequence 2002-01-16
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.
A sequence of number pairs 2002-01-10
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?

3-8
4-11
5-14
6-17
____
____
____
10-29
____
____
____

3, 6, 10, 15, 21 2001-11-29
From Patrick:
we are trying to find the expression to solve for the nth term in the pattern

3, 6, 10, 15, 21

Number sequences 2001-11-17
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, _, _, _.

2=the square root of (2 + the square root of (2 + the square root of (2 +...))) 2001-11-05
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, .......

1+2+3+...+1000 2001-10-01
From Louise:
Find a quick way to add all Intergers (whole Numbers) between 1 and 1000?
Find the pattern 2001-09-26
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,____,____,_____,_____,_____

Four sequences 2001-09-24
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...
1. DEGHNORY, EHILMU, HIILMTU, BEILLMRUY,...

2. 50, 33, 25, 20, 16, 14, 12,...

3. 1777, 1795, 1818, 1819, 1820, 1822, 1836, 1837..

4. A,H,I,M,O,T,...

Answered by Chris Fisher and Penny Nom.
Arithmetic sequences 2001-09-10
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 + (n-1)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.
A sequence 2001-08-25
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.

A sequence defined recursively 2001-05-01
From A student:
A sequence s is defined recursively as follows:

s0=1
s1=2
sk=2sk-2 for all integers

- Compute s2,s3,s4... to guess an explicit formula for the sequence sk.

A sequence of even terms 2001-04-29
From A student:
A sequence c is defined recursively as follows:

c0 = 2
c1 = 4
c2 = 6

ck= 5ck-3 for all integers

Prove that cn is even for all integers.

Answered by Leeanne Boehm and Penny Nom.
Geometric and arithmetic sequences 2001-01-26
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 2001-01-23
From Tami:
What is the sequence of the numbers 0,2,3,6,7,1,9,4,5,8
Some terms in a sequence 2001-01-15
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
Find the rule 2000-10-27
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.
A sequence question 2000-10-23
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!!!!

7 - - - - 77 2000-09-13
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 2000-08-25
From Wallace:
Prove that it is not possible to have the sum of the squares of 13 consecutive positive integers be a square.
Covering 1, 1/2, 1/3,... 2000-08-22
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?
Patterning and Sequencing 2000-07-05
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!

A sequence 2000-06-16
From Claire Hall:
Can you find the formula for the pattern 4,12,24,40,60
The number of seats in an auditorium 2000-05-16
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.
Looking for a pattern 2000-05-08
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.
Geometric sequences 2000-04-11
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!
Completing a sequence 2000-03-17
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 __ __

What's the next term? 2000-02-29
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 ??

Number sequences 1999-11-11
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. 1999-03-06
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!

Finding a rule for a sequence 1999-02-17
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.

What's the next term? 1998-11-12
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!

Sequences and series 1998-05-27
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.

Pay Phone Problem 1998-02-26
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.