A small auditorium has 10 rows of seats. There are 12 seats in the row and 16 seats in the second row the number of seats in a row continues to increase by 4 with each additional row. What is the total number of seats in the auditorium?

This problem can be solved through simple arithmetic progression

Let

a1 = the first term of the sequence

a (n) = the nth term of the sequence

n = number of terms

d = common difference

Sn = sum of all terms

given

a1 = 12

a2 = 16

n = 10

d = 16 - 12 = 4

@n = 10

a (n) = a1 + (n-1) d

a (10) = 12 + (9) 4

a (10) = 48 seats

Sn = (n/2) * (a1 + a (10))

Sn = 5 * (12 + 48)

Sn = 300 seats

Therefore the total number of seats is 300.