Question

Find $S_n$ for the geometric series described as $a=3,t_8=384,n=8$.

Answer 1

Given,

$t_n=a{r}^{n-1}$

$t_8=3\times r^{8-1}=384\Rightarrow r^7=128\Rightarrow r=2$

$S_n=\frac{a(r^n-1)}{r-1}$

$=\frac{3(2^8-1)}{2-1}$

$=765$