Answer
$2,\ 1,\ -1/2,\ -1/4,\ 1/8,\ 1/16,\ -1/32,\ -1/64,\ 1/128,\ 1/256$
Work Step by Step
$\left[\begin{array}{ll}
n & a_{n}\\ \\
1 & 2\\ \\
2 & (-1)^{2}(2)/2=1\\ \\
3 & (-1)^{3}(1)/2=-1/2\\ \\
4 & (-1)^{4}(-1/2)/2=-1/4\\ \\
5 & (-1)^{5}(-1/4)/2=1/8\\ \\
6 & (-1)^{6}(1/8)/2=1/16\\ \\
7 & (-1)^{7}(1/16)/2=-1/32\\ \\
8 & (-1)^{8}(-1/32)/2=-1/64\\ \\
9 & (-1)^{9}(-1/64)/2=1/128\\ \\
10 & (-1)^{10}(1/128)/2=1/256
\end{array}\right]$
