Chapter 12, Problem 17SGA

To determine

To find: the $n^{th}$ term of the geometric sequence.

Answer to Problem 17SGA

36044.8

Explanation of Solution

Given information:

  $\begin{array}{l}{a}_1=2.2\\ r=2\\ n=15\end{array}$

Calculation:

The ${15}^{th}$ term of the geometric sequence can be evaluated as shown below.

  $\begin{array}{c}{a}_n=a_1{r}^{n-1}\\ a_{15}=a_1{r}^{15-1}\left[\text{Put }n=15\right]\\ =a_1{r}^{14}\\ =2.2{\left(2\right)}^{14}\left[\text{Put the value of }{a}_1\text{ and }r\right]\\ =2.2\left(16384\right)\\ =36044.8\end{array}$

Thus ${15}^{th}$ term of the geometric sequence is 36044.8.