Chapter 9.3, Problem 43E

To determine

To Find : The Indicated term of the sequence

  $\text{3rd term : }{a}_1=16,a_4=\frac{27}{4}$

Answer to Problem 43E

The 3^rd term is $a_3=9$

Explanation of Solution

Given: Write the indicated term of the Geometric Sequence

  $\text{3rd term : }{a}_1=16,a_4=\frac{27}{4}$

Formula Used :

Nth term of the Geometric Sequence :

  $a_n=a_1{r}^{n-1}$

  $\begin{array}{l}\text{3rd term : }{a}_1=16,a_4=\frac{27}{4}\\ a_4=a_1{r}^3\\ \frac{27}{4}=16r^3\\ \frac{3}{4}=r\\ a_n=a_1{r}^{n-1}\\ a_n=16{\left(\frac{3}{4}\right)}^{n-1}\\ a_3=16{\left(\frac{3}{4}\right)}^{3-1}=16{\left(\frac{3}{4}\right)}^2=9\end{array}$

Hence , The 3^rd term is $a_3=9$

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