An auditorium has 30 rows, with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?
A) 1230
B) 600
C) 1170
D) 735

Question

Quizplus · Accepted Answer

The number of seats forms an arithmetic sequence starting with 10 seats in the first row, with each subsequent row having 2 more seats than the previous one. The total number of seats can be calculated using the formula for the sum of an arithmetic series: $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first $n$ terms, $a_1$ is the first term, $a_n$ is the nth term, and $n$ is the number of terms. Here, $n = 30$ rows, $a_1 = 10$ seats, and $a_n = 10 + 2(30-1) = 10 + 58 = 68$ seats. Plugging these values into the formula gives $S_{30} = \frac{30}{2}(10 + 68) = 15 \times 78 = 1170$ seats.

An Auditorium Has 30 Rows, with 10 Seats in the First