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36 votes
36 votes
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?

User Debasish Mitra
by
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1 Answer

19 votes
19 votes

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.

User Roberto Langarica
by
2.8k points