Chapter 9 - Conic Sections, Sequences, and Series - 9.5 Series - 9.5 Exercises - Page 746: 7

$(-5)+10+(-15)+20+(-25)+30=15$.

We need to sum the first six terms of the sequence whose general term is $a_{n}=5n(-1)^{n}$. This yields $\sum\limits^{6}_{n=1}(5n(-1)^{n})=[5(1)(-1)^{1}]+[5(2)(-1)^{2}]+[5(3)(-1)^{3}]+[5(4)(-1)^{4}]+[5(5)(-1)^{5}]+[5(6)(-1)^{6}]$ $=5(-1)+10(1)+15(-1)+20(1)+25(-1)+30(1)$ $=(-5)+10+(-15)+20+(-25)+30$ $=15$