Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 815: 61

$1185$ seats

Consider the arithmetic sequence: $a_1=25$ $n=30$ $d=1$ Determine the number of seats in the theater using the formula: $S_n=\dfrac{n(2a_1+(n-1)d)}{2}$ $S_{30}=\dfrac{30(2(25)+(30-1)(1))}{2}=\dfrac{30(79)}{2} =1185$