Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 815: 62

$2160$ seats

Consider the arithmetic sequence: $a_1=15$ $n=40$ $d=2$ Determine the number of seats in the theater using the formula: $S_n=\dfrac{n(2a_1+(n-1)d)}{2}$ $S_{40}=\dfrac{40(2(15)+(40-1)(2))}{2}=\dfrac{40(108)}{2} =2160$