Question

A theater has 26 rows of seats. The first row has 18 ​seats, the second row has 21 ​seats, the third row has 24 ​seats, and so on. How many seats are in the​ theater?

please help

Answer 1

In total, the theater seats 1442 people.

Given : The number of rows in the theater = 26

The number of chairs in first row = 18

The number of rows in the second row = 21

The number of rows in the third row = 24

The common difference in the number of chairs for the consecutive rows
`=3`

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:

`\text{S}_{\text{n}}=\frac{\text{n}}{2}(2\text{a}+(\text{n}-1)\text{d})`, where a is the umber of chairs in first row .

Put a = 18, d = 3 and n = 26, we get

`\text{S}_{\text{26}}=\frac{\text{26}}{2}(2(18)+(26-1)\text{3})=1442`

Hence, In total, the theater seats 1442 people.