Question

Find the total number of seats of an amphitheater if it has 70 rows with 40 seats, 44 seats and 48 seats on the first, second and third rows respectively.

Answer 1

To get the total number of seats;

$=\frac{n} {2} (2a+(n-1)d)$ where $n$ is the total number of rows, $d$ is the common difference between the rows and $a$ is the number of seats in the first row.

a=40

n=70

d=4

$=\frac{70} {2} (2×40+(70-1)4)$

=38(80$+$ 276)

=38(356)

=12,460 seats.