Chapter 8.1, Problem 54E

To determine

To Find: How many pushup will do in the ninth week. Justify.

Answer to Problem 54E

  $105$

Explanation of Solution

Given: You begin an exercise program. The first week you do $25$ pushups. Each week you do $10$ more pushups than the previous week.

Number of pushups in the first week= $25$

Pushups increased each week= $10$

The pattern form is

  $\begin{array}{l}{a}_1=25\\ a_2=1(10)+25\\ a_3=2(10)+25\\ .\\ .\end{array}$

i.e.

  $\begin{array}{l}{a}_n=10(n-1)+25\\ a_n=10n+15\end{array}$

Now

We have to find the number of pushups in ninth week

Substitute $n=9$

  $\begin{array}{l}{a}_n=10n+15\\ a_9=10(9)+15\\ a_9=90+15\\ a_9=105\end{array}$

Hence, $105$ pushups.