Chapter 9.3, Problem 33E

To determine

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

  $a_1=100,r=e^x,n=9$

Answer to Problem 33E

The nth term of the Sequence is $a_n=100{\left(e^x\right)}^{n-1}$ and the 10^th term is $a_9=100e^{8x}$

Explanation of Solution

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

  $a_1=100,r=e^x,n=9$

Formula Used :

Nth term of the Geometric Sequence :

  $a_n=a_1{r}^{n-1}$

  $\begin{array}{l}{a}_1=100,r=e^x,n=9\\ a_n=a_1{r}^{n-1}\\ a_n=100{\left(e^x\right)}^{n-1}\\ then\\ n=9\\ a_9=100{\left(e^x\right)}^{9-1}=100{\left(e^x\right)}^8=100e^{8x}\end{array}$

Hence , the nth term of the Sequence is $a_n=100{\left(e^x\right)}^{n-1}$ and the 9^th term is $a_9=100e^{8x}$

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