# Math Help - Gemoetric Series

1. ## Gemoetric Series

Find the sum of the first ten terms of a GP which has 3rd term 20 and 8th term 640.

2. The nth tem of a geometric series is given by

$a_{n}=a_{1}r^{n-1}$

So, with the given info we have:

$a_{3}=a_{1}r^{2}=20$

$a_{8}=a_{1}r^{7}=640$

The nth partial sum is given by:

$S_{n}=a_{1}\cdot\frac{1-r^{n}}{1-r}$

So, the sum of the first 10 terms is

$S_{10}=a_{1}\cdot\frac{1-r^{10}}{1-r}$

Solve the first two equations for $a_{1} \;\ and \;\ r$

Then, use them in the partial sum equation.