Chapter 6, Problem 29CR

To determine

To write:An equation for the nth term of the geometric sequence. Then find $a_9$

Answer to Problem 29CR

An equation for nth term of the sequence is $a_n=4^{n-1}$

  $a_9=65536$

Explanation of Solution

Given information:The sequence $1,4,16,\mathrm{64...}$

Calculation:The first term is 1 and the common ratio is 4.

  $a_n=a_1{r}^{n-1}$

  $\begin{array}{l}$ a_n=1{(4)}^{n-1}$\Rightarrow a_n=4^{n-1}\end{array}$

Thus, an equation for nth term of the sequence is $a_n=4^{n-1}$

Using the equation to find the 9^th term,

  $\begin{array}{l}{a}_n=4^{n-1}\\ \Rightarrow a_9=4^{9-1}\\ \Rightarrow a_9=4^8\\ \Rightarrow a_9=65536\end{array}$

Thus, 9^th term of the geometric sequence is $a_9=65536$