Chapter 9 - Conic Sections, Sequences, and Series - 9.5 Series - 9.5 Exercises - Page 747: 25

$-7460$

$a_{n+1}-a_n=-9(n+1)-2-(-9n-2)=-9$ Since the difference between consecutive terms is constant, the given sequence is arithmetic. The formula for the finite sum of the arithmetic sequence is: $S_{n}=\frac{n(a_{1}+a_{n})}{2}$ $a_{n}=-9n-2$ $a_{1}=-9(1)-2=-11$ . $a_{40}=-9(40)-2=-362$ $S_{40}=\frac{40(a_{1}+a_{40})}{2}=\frac{40(-11-362)}{2}=-7460$