Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 815: 67

$1647$ seats

Consider the arithmetic sequence: $a_1=35$ $n=27$ $d=37-35=39-37=2$ Determine the number of seats in the theater using the formula: $S_n=\dfrac{n(2a_1+(n-1)d)}{2}$ $S_{27}=\dfrac{27(2(35)+(27-1)(2))}{2}=\dfrac{27(122)}{2} =1647$