Chapter 9.3, Problem 46E

To determine

To Find : The Indicated term of the sequence

  $\text{5th term : }{a}_2=2,a_3=-\sqrt{2}$

Answer to Problem 46E

The 5^thterm $a_5=2$

Explanation of Solution

Given: Write the indicated term of the Geometric Sequence

  $\text{5th term : }{a}_2=2,a_3=-\sqrt{2}$

Formula Used :

Nth term of the Geometric Sequence :

  $a_n=a_1{r}^{n-1}$

  $\begin{array}{l}\text{5th term : }{a}_2=2,a_3=-\sqrt{2}\\ a_3=a_2{r}^1\\ -\sqrt{2}=2r^1\\ -\frac{\sqrt{2}}{2}=r^1\\ r=-\frac{1}{\sqrt{2}}\\ a_5=\frac{a_3}{r}=\frac{-\sqrt{2}}{-\frac{1}{\sqrt{2}}}=-\sqrt{2}.\frac{-\sqrt{2}}{1}=2\\ \end{array}$

Hence , The5^thterm is $a_5=2$

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