Chapter 9.3, Problem 32E

To determine

To Find : The nth term of the Geometric Sequence and its Indicated term

  $a_1=64,r=-\frac{1}{4},n=10$

Answer to Problem 32E

The nth term of the Sequence is $\begin{array}{l}{a}_n=64{\left(-\frac{1}{4}\right)}^{n-1}\\ \end{array}$ and the 10^th term is $a_{10}=-\frac{64}{262,144}$

Explanation of Solution

Given: Write an expression for the nth term of the Geometric Sequence . Then find the indicated term

  $a_1=64,r=-\frac{1}{4},n=10$

Formula Used :

Nth term of the Geometric Sequence :

  $a_n=a_1{r}^{n-1}$

  $\begin{array}{l}{a}_1=64,r=-\frac{1}{4},n=10\\ a_n=a_1{r}^{n-1}\\ a_n=64{\left(-\frac{1}{4}\right)}^{n-1}\\ then\\ n=10\\ a_{10}=64{\left(-\frac{1}{4}\right)}^{10-1}=64{\left(-\frac{1}{4}\right)}^9=-\frac{64}{262,144}\end{array}$

Hence , the nth term of the Sequence is $\begin{array}{l}{a}_n=64{\left(-\frac{1}{4}\right)}^{n-1}\\ \end{array}$ and the 10^th term is $a_{10}=-\frac{64}{262,144}$

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