Chapter 9 - Conic Sections, Sequences, and Series - 9.5 Series - 9.5 Exercises - Page 746: 8

$(-2)+4+(-6)+8+(-10)+12+(-14)=-8$.

We need to sum the first seven terms of the sequence whose general term is $a_{n}=2n(-1)^{n}$. This yields $\sum\limits^{7}_{n=1}(2n(-1)^{n})=[2(1)(-1)^{1}]+[2(2)(-1)^{2}]+[2(3)(-1)^{3}]+[2(4)(-1)^{4}]+[2(5)(-1)^{5}]+[2(6)(-1)^{6}]+[2(7)(-1)^{7}]$ $=2(-1)+4(1)+6(-1)+8(1)+10(-1)+12(1)+14(-1)$ $=(-2)+4+(-6)+8+(-10)+12+(-14)$ $=-8$