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?

Question

asked Nov 23, 2023 234k views

1 Answer

Mjhasbach · Answer 1 · 2023-11-27T18:37:19+0000

Answer:

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.