Question

Find the ninth term of the GP: $1,4,16,64,....$.

Answer 1

Calculate the ninth term of GP:

Given series, $1,4,16,64,....$.

The first term of the geometric progression, $a_1=1$.

As the given series is in geometric progression, thus the consecutive terms have a common ratio.

The common ratio of the geometric progression, $r=\frac{a_2}{a_1}=\frac{4}{1}=4$.

Thus, the $n^{\mathrm{th}}$ term of the geometric progression can be given by, $a_n=a_1{\left(r\right)}^{n-1}=1{\left(4\right)}^{n-1}=4^{n-1}$.

Hence, the ninth term of the given series, $a_9=4^{9-1}=4^8=65536$.

Therefore, the ninth term of the GP is $65536$.