Question

A theater has 22 rows of seats. The first row has 18​ seats, the second row has 20 ​seats, the third row has ​22 seats, and so on. How many seats are in the​ theater?

Answer 1

1078

Explanation:

Total no of rows (n) = 22

Since, 18, 20, 22 ..... forms an arithmetic sequence with first term (a) = 18 and common difference (d) = 2.

We need to find: Total no of seats in the theatre
`(S_(22)).`

Formula to be used:

`S_(n)= (n)/(2)\bigg[2a+(n-1)d\bigg]`

Plug the values of a, d and n in the above formula, we find:

`\implies S_(22)= (22)/(2)\bigg[2(28)+(22-1)(2)\bigg]`

`\implies S_(22)=11[56+(21)(2)]`

`\implies S_(22)=11[56+42]`

`\implies S_(22)=11[98]`

`\implies S_(22)=1078`

Thus, there are total 1078 seats in the theatre.