# Math Help - geometric series

1. ## geometric series

hi

I know the answer to this question is 9 but I am not sure how to get there.

I know that there is probably a really simple method but at the moment I am making a mistake somewhere,

2+4+8+...+512

find the number of terms in the geometric series?

thanks

2. Hello,

I don't really understand. If it was a geometric series, it would have been 1/2 + 1/4 + 1/8 + ... + 1/512

If so, you can say that 512 is 2^9

3. ## geometric series re

those are the number that it shows in the book, could be wrong though.

I know that 2^9 is 512 but how do I find the number of terms in the series- is there a really simple step that I am missing?

thanks

4. the nth term of a geometric series is ar^(n-1). since the last term is 512 and we know that a=2 and r=2

substituting values

2(2)^(n-1) = 512
2^(n-1) = 256
2^(n-1) = 2^8

compare both sides

n-1 = 8
n= 9

hence the last term is the 9th term

5. Originally Posted by soso
those are the number that it shows in the book, could be wrong though.

I know that 2^9 is 512 but how do I find the number of terms in the series- is there a really simple step that I am missing?

thanks
Well,

You have :

2^1, 2^2, 2^3, ..., 2^9

This makes 9 termes

6. $\sum\limits_{k = 1}^N {a^k } = \frac{{a - a^{N + 1} }}{{1 - a}},\quad N = 9\,\& \,a = 2
$

7. ## thanks

thanks for the help