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?
Anyone is here



​

Answer 1

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