Question

Which term of the G.P. $2,8,32$.. upto n terms is $131072$?

Answer 1

$2,8,32,.........$

$\Rightarrow a=2,r=4$

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

$T_n=131072$

$\left(2\right)(4{)}^{n-1}=131072$

$\Rightarrow (4{)}^{n-1}=65536$

$\Rightarrow (4{)}^{n-1}=(4{)}^8$

$\therefore n-1=8\Rightarrow n=9$

$\therefore n=9$