Chapter 4, Problem 8CT

(a)

To determine

To find: The number of seats in row $25$

Answer to Problem 8CT

The number of seats in row $25$ is $114seats$

Explanation of Solution

Given:

The first row of an auditorium has $42$ seats.

Each row after the first has three more seats than the row before it.

Calculation:

First term $a1=42$

Common difference $d=3$

Consider the equation for an arithmetic sequence

  $an=a1+(n-1)d$

Now, the number of seats in row $25$ is

  $\begin{array}{l}a25=42+(25-1)3\\ =42+(24)3\\ =42+72\\ =114\end{array}$

Conclusion:

Hence, the number of seats in row $25$ is $114seats$

(b)

To determine

To find: The row that has $90$ seats

Answer to Problem 8CT

The $17th$ row has $90$ seats

Explanation of Solution

Given:

The first row of an auditorium has $42$ seats.

Each row after the first has three more seats than the row before it.

Calculation:

Consider

  $an=90$

Now, find the row number for $90$ seats using the equation for an arithmetic sequence

  $an=a1+(n-1)d$

Substitute the values

  $\begin{array}{l}90=42+(n-1)3\\ 90=42+3n-3\end{array}$

Take the variable at left side and find the value

  $3n=51$

Divide by $3$ on both sides

  $n=17$

Conclusion:

Hence, the $17th$ row has $90$ seats