Chapter SH, Problem 10.14EP

To determine

To find: The cost of the system after 8 weeks.

Answer to Problem 10.14EP

The cost of the system is $\$255$ .

Explanation of Solution

Given:

Dustin saved one dollar in the first week and each of the following weeks he saved twice as much as the week before.

Calculation:

From the given information the geometric series is $1,2,4,8,16,32,64,128$ .

Find the common ratio.

  $\begin{array}{c}\frac{2}{1}=2\\ \frac{4}{2}=2\\ \frac{8}{4}=2\\ \frac{16}{8}=2\\ ⋮\end{array}$

Find the sum of the geometric series.

  $\begin{array}{c}{S}_n=\frac{a\left(r^n-1\right)}{r-1}\\ =\frac{1\left(2^8-1\right)}{2-1}\\ =2^8-1\\ =255\end{array}$

Therefore, the cost of the system is $\$255$ .