Chapter 11.6, Problem 26WE

To determine

To calculate:

First three terms of the infinite geometric series.

Answer to Problem 26WE

First three terms of the infinite geometric series are $75,30,12$ .

Explanation of Solution

Give information:

  $r=\frac{2}{5},S=125$

Calculation:

Given is $r=\frac{2}{5},S=125$ ,

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

  $S=\frac{t_1}{1-r}$

Here, $r=\frac{2}{5},S=125$

Solve for $t_1$ ,

  $\begin{array}{l}S=\frac{t_1}{1-r}\\ 125=\frac{t_1}{1-\left(\frac{2}{5}\right)}\\ 125=\frac{t_1}{1-\left(\frac{2}{5}\right)}\\ 125=\frac{t_1}{0.6}\\ \left(125\right)\left(0.6\right)=t_1\\ t_1=75\end{array}$

First three terms by using the ratio,

First term is $75$

Second term is $75\left(\frac{2}{5}\right)=30$

Third term is $30\left(\frac{2}{5}\right)=12$

Thus, First three terms of the infinite geometric series are $75,30,12$ .