Question

I will post the question below... Math question...

Answer 1

If \(a _{k}=5+5^2+5^3+5^4+.....5^k\) for which of the following values of k will \(a _{k}\) be divisible by 10?

Answer 2

A) 35
B)51
C)75
D)88
E)91

Answer 3

i would look for a pattern

Answer 4

i can make a guess, my guess is that k has to be even, but i could be wrong
look for a pattern and see

Answer 5

@satellite73 The answer is 88... and that is the only even answer choice..

Answer 6

BTW this is not a homework or test question...

Answer 7

I just wanted to know how to solve it if I ever encounter a problem like it...

Answer 8

I got this question from Pg 184 Q132
http://www.amazon.com/Problems-arranged-Topic-Difficulty-Warner/dp/B00C7F2XNI/ref=sr_1_7?ie=UTF8&qid=1413748042&sr=8-7&keywords=320+sat+math+problems+arranged+by+topic+and+difficulty+level

Answer 9

The question is supposed to be a level 5 Number Theory question...

Answer 10

\[x+x^2+x^3+\cdots+x^n=\sum_{k=1}^nx^k = \dfrac{x^{n+1}-1}{x-1}\]
Check here: http://mikestoolbox.com/powersum.html

Answer 11

Maybe that helps?

Answer 12

Yes...

Answer 13

Find the sum: Geometric progression = \[\frac{5}{4} (5^k-1)\]

For this to be divisible by 10, \[\frac{5^k-1}{4} ~~must~~be~~even!\]
\[\frac{5^k-1}{4} = 2n\] [n is an integer]
\[5^k = 8n + 1\]
Find what k is.

Answer 14

I take that as no, since it seem obvious to you.

Answer 15

Only the even 'k's will be correct.
But this proof is very crude. There are better ways with Number Theory, probably with mod, but I am not proficient in Number Theory.

Answer 16

Well my teacher explained it just like but I wasn't sure.. But now you guys clarified it.. ^_^