Chapter 14, Problem 2MPS

To determine

To Find: The total prize won by Rico.

Answer to Problem 2MPS

The total prize won is $\$6890$ .

Explanation of Solution

Given:

The Rico won the prize of $\$5$ on week, $10 the second week and $15 the third week.

The prizes are won for 52 weeks.

Calculation:

Consider the formula for the arithmetic progression is,

  $a_n=a_1\left(n-1\right)d$

Then,

  $\begin{array}{c}{a}_n=5+\left(52-1\right)5\\ =260\end{array}$

The total prize won in the 52^nd week is $260.

Then the total prize won is obtained as,

  $\begin{array}{c}{S}_{52}=\frac{52\left(5+260\right)}{2}\\ =\$6890\end{array}$