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.