Question

A theater has 32 rows. The first row has 18 seats, second row has 21 seats, third row

has 24 seats, and so on. Determine the total number of seats in the theater.

Answer 1

2064

Explanation:

18 + 21 + 24 + ...

This is an arithmetic series with first term 18 and common difference 3.

The nth term is

18 + 3(n - 1)

The 32nd term is the number of seats in the 32nd row:

18 + 3(32 - 1) = 18 + 3(31) = 18 + 93 = 111

The sum of the series is:

n/2(a + L) = (32/2)(18 + 111) = 2064