Question

determine the seating capacity of an auditorium with 46 rows if there are 18 seats in the first row, 21 in the second, and 24 in the third and so on

Answer 1

The first row has 18 seats and the last row hae 18 + 3*45 = 171 seats
The average is 85.5 seats. Multiply that by 46 for the total: 3933.

There is another way to do it:
46*18 + 3*(1 + 2 + 3 + ...45)
= 828 + (3/2)(45*46)
= 828 + 3105 = 3933

Here, I used the rule that
(1+2+3+...N) = (N)(N+1)/2