Question

Which term of the GP.
$2,8,32,....$ is $512$?

Answer 1

Given G.P $2,8.32,\dots \dots$

$a=2$, $r=\frac{8}{2}=4$,

Let $T_n=512$

$a{r}^{(n-1)}=512$

${24}^{n-1}=512$

$4^{n-1}=256$

$4^{n-1}=(4{)}^4$

$n-1=4$

$\Rightarrow n=5$

$\therefore 5^{th}$ term is $512$