Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-A theater has 36 rows with 26 seats in the first row, 30 in the second row, 34 in the third row, and so forth. How many seats are in the theater?
A) 3456 seats
B) 3528 seats
C) 6912 seats
D) 7056 seats

Question

Quizplus · Accepted Answer

The sum of the first n terms of an arithmetic sequence is given by the formula:$$S_n = \frac{n}{2}(a_1 + a_n)$$where $a_1$ is the first term, $a_n$ is the nth term, and $n$ is the number of terms.In this problem, $a_1 = 26$, $a_n = 26 + (36 - 1)4 = 154$, and $n = 36$.Substituting these values into the formula, we get:$$S_{36} = \frac{36}{2}(26 + 154) = 18(180) = 3240$$Therefore, the total number of seats in the theater is 3240.

Use the Formula for the Sum of the First N