Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.1 Sequences - 12.1 Assess Your Understanding - Page 808: 78

$-2376$

I know that $\sum_{k=1}^{n} (k)=\frac{n(n+1)}{2}.$ Hence $\sum_{k=8}^{40} (-3k)=\sum_{k=1}^{40} (-3k)-\sum_{k=1}^{7} (-3k)=-3\sum_{k=1}^{40} (k)-(-3)\sum_{k=1}^{7}(k)=-3\frac{40(40+1)}{2}-(-3)\frac{7(7+1)}{2}=-2460+84=-2376$