Chapter 9.2, Problem 25PPSE

Solution

To determine the amount in the bank account at the end of the ninth week.

Amount at the end of the ninth week is $\$135.$

Given:

It is given that the amount in the bank amount at the end of second week is $\$30$ and at the end of third week is $\$45.$

Formula Used:

An explicit formula for the arithmetic sequence is given by:

  $a_n=a+\left(n-1\right)d$

Calculation:

A student deposits same amount in the account each week.Sothat according to the given information, the amount at the end of first week is $\$15.$

Hence, the arithmetic sequence is:

  $15,30,45,\dots$

with

  $a_1=15,a_2=30,a_3=45$

The common difference is given as:

  $\begin{array}{l}d=a_2-a_1\\ \Rightarrow d=30-15\\ \Rightarrow d=15\end{array}$

Now, using an explicit formula to find the amount for ninth week as:

  $\begin{array}{l}{a}_n=a+\left(n-1\right)d\\ \Rightarrow a_9=15+\left(9-1\right)15\\ \Rightarrow a_9=15+8\left(15\right)\\ \Rightarrow a_9=15+120\\ \Rightarrow a_9=135\end{array}$

Hence, the amount in the bank account at the end of ninth week is $\$135.$