The seating in a certain theater is arranged so that there are 44 seats in row 1, 45 seats in row 2, 46 seats in row 3, and so on. If there are 25 rows, what is the total revenue is the average ticket price is $8.00 per seat and the theater is sold out?
A) $11,200.00
B) $272.00
C) $6800.00
D) $448.00

Question

Quizplus · Accepted Answer

The total number of seats can be found using the formula for the sum of an arithmetic series, $S_n = \frac{n}{2}[2a + (n-1)d]$, where $n$ is the number of terms, $a$ is the first term, and $d$ is the common difference. Here, $n = 25$, $a = 44$, and $d = 1$. So, $S_{25} = \frac{25}{2}[2(44) + (25-1)(1)] = \frac{25}{2}[88 + 24] = \frac{25}{2}[112] = 1400$ seats. The total revenue is $1400 \times 8 = \$11,200.00$.

The Seating in a Certain Theater Is Arranged So That