Chapter 11.3, Problem 17PPS

To determine

Find the height did the river rise in five days.

Answer to Problem 17PPS

93 inches

Explanation of Solution

Given:

Heavy rain in Brieanne`s town caused the river to rise. The river rose three inches the first day, and each day after rose twice as much as the previous day. How much did the river rise in five days.

Concept Used:

The river rose three inches the first day, so the first term of the series is 3

Each day after rose twice as much as the previous day, so the common difference is 2.

Number of days = 5

Calculation:

  $a_1=3,r=2,n=5,\text{Find}{\text{S}}_{\text{n}}$

  $\begin{array}{l}{\text{S}}_{\text{n}}=\frac{a_1(r^n-1)}{r-1}\\ {\text{S}}_{\text{n}}=\frac{3(2^5-1)}{2-1}=\frac{3·31}{1}=93\end{array}$

Thus, the river rises 93 inches in five days.