Question

The Drury Lane Theater has 10 seats in the first row and 38 rows in all. Each successive row contains one additional seat. How many seats are in the theater?


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Answer 1

1083 seats

Explanation:

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arithmetic sequence

a1 = 10

an = an-1 + 1 = a1 + (n-1)×1 = 10 + (n-1) = 9 + n

a38 = 9 + 38 = 47 seats

the sum of such an arithmetic sequence

n×(a1 + an)/2

in our case

38×(10 + 47)/2 = 19×57 = 1083 seats