16. The sequence $a _ { n }$ is given by the rule:
$$\begin{aligned}
a _ { 1 } & = 2 \\
a _ { n + 1 } & = a _ { n } + ( - 1 ) ^ { n } \text { for } n \geq 1
\end{aligned}$$
What is
$$\sum _ { n = 1 } ^ { 100 } a _ { n }$$
A 150\\
B 250\\
C - 4750\\
D 5150\\
E $\quad 4 \left( 1 - \left( \frac { 1 } { 2 } \right) ^ { 100 } \right)$\\
F $\quad 4 \left( \left( \frac { 3 } { 2 } \right) ^ { 100 } - 1 \right)$\\