Question

A theater has 25 rows of chairs. The first row has 18 chairs, the second has 22, and the third has 26, and so on. In total, the theater seats ____ people.

Answer 1

the answer would be 1,650.

Answer 2

Answer: In total, the theater seats 1650 people.

Explanation:

Given : The number of rows in the theater = 25

The number of chairs in first row = 18

The number of rows in the second row = 22

The number of rows in the third row = 26

The common difference in the number of chairs for the consecutive rows =

`=4`

Thus its a Arithmetic progression.

Let n be the number of rows and d be the common difference , then the total number of chairs in n rows is given by :-

`S_n=(n)/(2)(2a+(n-1)d)`, where a is the umber of chairs in first row .

Put a = 18, d=4 and n = 25, we get

`S_(25)=(25)/(2)(2(18)+(25-1)4)=1650`

Hence, In total, the theater seats 1650 people.