







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. 





1 + 2 + 3 + ... + (2n  1) 
20150101 

From Brian: Hi Maths Central
My wife presented me with a query which may have a simple answer, but one that I can’t deduce or explain.
Take the string of numbers, n=1,2,3,4,5…
It seems that n(2n1) = Sum((1…..(2n1))
e.g. for n=5, both 5 x 9 and Sum(1….9) equal 45, and so on for other values of n.
Could you please provide an explanation? Does it have an underlying reason and a name?
Look forward to your response.
Brian Answered by Penny Nom. 





An arithmetic progression 
20141119 

From Gbenga: In an A.P the difference between 8th and 4th term is 20. The 8th term is 1\2 times the 4th term . Find arithmetic progression.. 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. 





An arithmetic progression 
20140331 

From Japheth: The 3rd term of an A.P is 10 more than the first term while the fifth term is 15 more than the second term. Find the first term? 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. 





An Arithmetic Progression 
20131008 

From collins: In an A.P. the difference between the 8th and 4th term is 20 and the 8th is one and half times the 4th term... what is the common difference and the first term Answered by Penny Nom. 





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. 





An arithmetic progression 
20130706 

From ashok: the 4th and 10th term a.p respectively 7 and 19 find its 15th term..... Answered by Penny Nom. 





An arithmetic progression 
20130206 

From loberto: the 3rd term of an a.p is 10more than the 1st term,while the 5th term is 15more than the 2nd term,find the sum of the 8th and 15th terms of the a.p if the 7th term is 7times the 1st term 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 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. 





1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2 
20120127 

From Vicki: I am trying to find out how to do show how this proof was worked.
Here is the end result 1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2
This equation was used to find the number of white triangles in the Sierpinski Triangle Answered by Walter Whiteley. 





The 3rd term of an A.P is 10 more than the first term 
20111129 

From Olaniyan: the 3rd term of an A.P is 10 more than the first term while the fifth term is 15 more than the second term. Find the sum of the 8th and 15th terms of the A.P if the if the 7th term is 7 times the first term. 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. 





The value after 30 years 
20101215 

From Abeth: At the end of every year, the owners of a building which costs 2, 500, 000 pesos deducts 15% from its carrying value as estimated at the beginning of the year. find the estimated value at the end of 30 years. Answered by Penny Nom. 





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 
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 geometric progression 
20090516 

From sweta: find the ratio of GP if the first term is 1 and the sum of third and fifth term is 90. Answered by Penny Nom. 





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. 





Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: 
20050718 

From Ladis: Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: p=p, q=p+d and r= p+2d. Prove that d is divisible by 6. Answered by Chris Fisher. 





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. 





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

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





The sum of some positive integers 
20040607 

From A student: Find the sum of all positive integers not greater than 10000 that are divisible by neither 3 nor 7. Answered by Penny Nom. 





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. 





7+8+9+...+1000 
20020911 

From Shirley: My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers? Answered by Penny Nom. 





Arithmetic progressions 
20020424 

From David: I have been searching everywhere for the formula to mathamatical progression. Answered by 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. 





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. 





Arithmetic Progressions 
19981112 

From Gerry Boser: It has been years since I was in school and I can't remember if there is a formula for the following problem: If you deposit $1.00 on the first day of the month, $2.00 on the second day, $3.00 on the third day . . $31.00 on the last day of the month, how much do you have in the bank? Now will this formula also work if it was, $0.25 (then day two you would deposit 2x $0.25 or $0.50, day three you would deposit 3x $0.25, $0.75. . . ). Will it work with any denomination?? Thank you for your time. I promise I'll write this one down for future reference. . . Answered by Penny Nom. 





Dividing a Class 
19981001 

From Tom Barker: My eighth grade niece called with the following homework problem: A teacher wanted to divide her class into equally numbered groups. She tried to divide the class into groups of two, but was one student short. She tried to divide the class into groups of five, but was one student short. She tried to divide the class into groups of seven and was successful. What is the least number of students that were in her class? I know the answer is 49, but don't know how to prove it. I must be getting old if I can't solve eighth grade math problems. Your assistance would be appreciated. Answered by Penny Nom. 





Progression arithmétique 
20080108 

From parrot: Bonjour je suis en 6ème et j'ai besoin d'aide pour un problème de math.
Donc voila mon problème :
Un renard a mangé 100 grains de raisins pendant une periode de 5 jours.
Chaque jour, il a mangé six grains le plus que le jour précédent.
Quel est le nombre de grains mangés le premier jour ? Answered by Claude Tardif. 

