Chapter 11.6, Problem 33SR

To determine

To find: The $a_n$ of the geometric sequence.

Answer to Problem 33SR

The $a_n$ of the geometric sequence is $1$ .

Explanation of Solution

Given information:

The given values are,

  $\begin{array}{l}{a}_4=16\\ r=0.5\\ n=8\end{array}$

The first term is calculated as,

  $\begin{array}{l}{a}_4=a{r}^{4-1}\\ 16=a{\left(0.5\right)}^3\\ a=128\end{array}$

The $a_n$ of the geometric sequence is calculated as,

  $\begin{array}{c}{a}_n=a{r}^{n-1}\\ =\left(128\right){\left(0.5\right)}^{8-1}\\ =1\end{array}$

Thus, the $a_n$ of the geometric sequence is $1$ .