Question

A concert hall has 12 seats in the first row, 14 seats in the second row, 16 seats in the third row, and so on. If the pattern continues, how many seats are in the first 12 rows?

Answer 1

Given:

The number of seats in the first row is a₁ = 12.

The series of the increasing number of seats is 12, 14, 16......

The objective is to find the total number of seats in the first 12 rows.

Explanation:

The difference between the number of seats in each row can be calculated by the difference between the successive terms of the series.

$\begin{gathered} d=14-12=2 \\ d=16-14=2 \end{gathered}$

The number of rows to be calculated is n = 12.

To find the number of seats:

The number of seats presents in the first 12 rows can be calculated as,

$S_n=\frac{n}{2}\lbrack2a_1+(n-1)d\rbrack$

On plugging the obtained values in the above equation,

$\begin{gathered} S_{12}=\frac{12}{2}\lbrack2(12)+(12-1)2\rbrack \\ =6\lbrack24+11(2)\rbrack \\ =6(46) \\ =276 \end{gathered}$

Hence, the total number of seats in the first 12 rows is 276.