Question

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

Answer 1

Given G.P., $2,8,32,...$ upto $n$ terms.
Here, first term $a=2$,
common ratio $r=\frac{8}{2}=4$ and $n^{th}$ term $=131072$

We know $a_n=a{r}^{n-1}$
$\Rightarrow 131072=2\times 4^{n-1}$
$\Rightarrow \frac{131072}{2}=4^{n-1}$
$\Rightarrow 4^{n-1}=65536$
$\Rightarrow 4^{n-1}=(4{)}^8$
On comparing powers, we get
$n-1=8$
$\therefore n=9$

Hence, $131072$ is the $9^{th}$ term of the G.P.