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

Answer:

1078

Step-by-step 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:

$S_{n}= \frac{n}{2}\bigg[2a+(n-1)d\bigg]$

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

$\implies S_{22}= \frac{22}{2}\bigg[2(28)+(22-1)(2)\bigg]$

$\implies S_{22}=11[56+(21)(2)]$

$\implies S_{22}=11[56+42]$

$\implies S_{22}=11[98]$

$\implies S_{22}=1078$

Thus, there are total 1078 seats in the theatre.