The first row in a theatre contains 7 seats, the second row contains 11 seats, and the third row contains 15 seats. If the theatre contains 1914 seats total, how many rows of seats are in the theatre?

Question

The first row in a theatre contains 7 seats, the second row contains 11 seats, and the third row contains 15 seats. If the theatre contains 1914 seats total, how many rows of seats are in the theatre?

I put down the formula Zn=n/2(2(n1)+(n-1)d)

Answer 1

This problem cannot be solved with these values.

The formula for the sum of this series is

Sn = (n / 2) (2a + d(n-1))

Substituting Sn = 1914, a = 7, d = 4 gives the following equation

1914 = (n / 2) ( 2(7) + 4(n-1))

This equation does not have a whole number solution. Therefore these values are not valid for this situation.

Answer 2

S_n = (n / 2)(2a₁ + (n - 1)d)

S_n = 1914

a₁ = 7

d = 4

Can you substitute values and solve for n?