Chapter 11.1, Problem 31PPS

To determine

Find the number of seats is in the last row of the theater.

Answer to Problem 31PPS

The number of seats in the last row is 74.

Explanation of Solution

Given:

There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater?

Concept Used:

There are 28 seats in the front row of a theater, so the first term of the sequence is 28.

Each successive row contains two more seats than the previous row; this means the common difference is 2.

Number of rows = 24

Calculation:

We have all of the information to use the general nth term formula $a_n=a_1+(n-1)d$ for an arithmetic sequence.

We know the row number that we are calculating is 24 and the number in the first row is 28. The common difference is 2.

  $a_1=28\text{and}d=2\text{and}n=24$

Now solve for

  $\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{24}=28+(24-1)·2\\ a_{24}=28+46\\ a_{24}=74\end{array}$ Last row means the number of seats in 24^th row is 74.

Thus, the number of seats in the last row is 74.