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Leokris [45]
2 years ago
12

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

any seats are in the theater?
Anyone is here



​
Mathematics
1 answer:
densk [106]2 years ago
3 0

Answer:

1083 seats

Step-by-step explanation:

this is an arithmetic sequence :

an = an-1 + c

in our case

a1 = 10 (10 seats in the first row)

a2 = a1 + 1 = 10 + 1 = 11

a3 = a2 + 1 = a1 + 1 + 1 = 10 + 1 + 1 = 12

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

a38 = a1 + 37 = 10 + 37 = 47 seats.

altogether this means the sum of the arithmetic sequence of a1 to a38.

the general sum of an arithmetic sequence from a1 to an is

n×(a1 + an)/2

in our case

38×(10 + 47)/2 = 19×57 = 1083 seats

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