Question

If the $n^{\text{th }}$ term of a G.P. $2,8,32,\dots .$. is $131072$ , then the value of $n$ is

• A. 8
• B. 9
• C. 10
• D. 11

Answer 1

Answer: (A)

$\because 131072$ be the $n^{\text{th }}$ term of given G.P.
Therefore, $131072=a_n=2(4{)}^{n-1}(\because a=2$ and $r=4)$
$\Rightarrow 65536=(4{)}^{n-1}$
$\Rightarrow 4^8=4^{n-1}$
$\Rightarrow 8=n-1$
$\Rightarrow n=9$
Hence, $131072$ is the $9^{\text{th }}$ term of the G.P. .