A theater has 30 seats in the first row, 33 seats in the second row, 36 seats in the third row, and so on in the same increasing pattern. If the theater has 15 rows of seats, how many seats are in the theater?

Answer 1

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence (an is given by:

an = a1 + ( n - 1 ) * d

This sum :

S = n * [ 2 a1 + ( n - 1 ) * d ] / 2

In this case :

a1 = 30

d = 3

n = 15

S = n * [ 2 a1 + ( n - 1 ) * d ] / 2

S = 15 * [ 2 * 30 + ( 15 - 1 ) * 3 ] / 2 =

15 * ( 60 + 14 * 3 ) / 2 =

15 * ( 60 + 42 ) / 2 =

15 * 102 / 2 = 1530 / 2 = 765

765 seats

Answer 2

how do you round to the nearest gram