Chapter 11.6, Problem 24WE

To determine

To calculate:

First three terms of the infinite geometric series.

Answer to Problem 24WE

First three terms of the infinite geometric series are $40,32,25.6$ .

Explanation of Solution

Give information:

  $t_1=40,S=200$

Calculation:

Given is $t_1=40,S=200$ ,

Use the formula of the sum of an infinite geometric series,

  $S=\frac{t_1}{1-r}$

Here, $S=200,t_1=40$

Solve for $r$ ,

  $\begin{array}{l}S=\frac{t_1}{1-r}\\ 200=\frac{40}{1-r}\\ 200\left(1-r\right)=40\\ 200-200r=40\\ 200-40=200r\\ 160=200r\\ r=\frac{4}{5}\end{array}$

First three terms by using the ratio,

First term is $40$

Second term is $40\left(\frac{4}{5}\right)=32$

Third term is $32\left(\frac{4}{5}\right)=25.6$

Thus, First three terms of the infinite geometric series are $40,32,25.6$ .