Question

The Drury Lane Theater has 10 seats in the first row and 38 rows in all. Each successive row contains one additional seat. How many seats are in the theater?

Answer 1

Explanation:

Given : 10 seat in first row, and the seat will increase 1 by 1 as we go above.... (as we go to the next row) - total rows - 38

Solve ; 38 rows, 10 seat in first row, 1 seat increases each row....

Extra seats - 37,

So,

37 x 10 = 370

TOTAL SEATS = 370

Answer 2

1083 seats

Explanation:

The number of seats is an arithmetic series with first term 10 and common difference 1. We want to find the sum of 38 terms of the series.

Setup

The sum of n terms of an arithmetic series with first term a1 and common difference d is given by the formula ...

Sn = (2a1 +d(n -1))(n/2)

The sum of the series of interest is ...

S38 = (2(10) +1(38 -1))(38/2)

Total seats

The total number of seats in the theater can be found by evaluating the expression for S38:

S38 = (20 +37)(19) = 57×19 = 1083

There are 1083 seats in the theater.