Chapter 12.2, Problem 59AYU

Drury Lane Theater The Drury Lane Theater has 25 seats in the first row and 30 rows in all. Each successive row contains one additional seat. How many seats are in the theater?

To determine

To find: The Drury Lane Theater has 25 seats in the first row and 30 rows in all. Each successive row contains one additional seat. How many seats are in the theater?

Answer to Problem 59AYU

1185

Explanation of Solution

Given:

Total number of rows $=30$.

Number of seats in the first row $=25$.

Each successive row contains one additional seat.

Formula used:

The $n$th term of an arithmetic sequence can be found by the formula,

$a_n=a_1+\left(n-1\right)d$   (Formula 1)

Sum of the first $n$ terms of an arithmetic sequence,

$S_n=\frac{n}{2}\left[a_1+a_n\right]$   (Formula 2)

Calculation:

From the given data, we get $n=30,a_1=25,d=1$.

To find $a_n$:

$a_n=25+29=54$   (By formula 1)

So, the given sequence will be $25+26+27+\dots +54$.

Therefore, the number of seats $=\frac{30}{2}\left[25+54\right]$

$=15\times 79=1185$   (By formula 2)