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?

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

Formula to be used:

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

Thus, there are total 1078 seats in the theatre.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2