Thread: Gemoetric Series

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

The nth tem of a geometric series is given by

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

So, with the given info we have:

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

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

The nth partial sum is given by:

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

So, the sum of the first 10 terms is

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


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

Then, use them in the partial sum equation.