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Umnica [9.8K]
2 years ago
12

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 o

n. How many seats are in the​ theater?
Mathematics
1 answer:
morpeh [17]2 years ago
3 0

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.

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<u>Answer-</u>

\boxed{\boxed{\text{Mass}=10.0447256\ ton}}

<u>Solution-</u>

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