Consider the sequence 
$1,-2,3,-4,5,-6,\ldots,$
whose $n$th term is $(-1)^{n+1}\cdot n$. What is the average of the first $200$ terms of the sequence?
$\textbf{(A)}-\!1\qquad\textbf{(B)}-\!0.5\qquad\textbf{(C)}\ 0\qquad\textbf{(D)}\ 0.5\qquad\textbf{(E)}\ 1$
The average of a list is the sum of all numbers divided by the size of the list.
The sum of the list can be found by adding the numbers in pairs:  $(1 + -2) + (3 + -4) + ... + (199 + -200)$
The sum of each pair is $-1$, and there are $100$ pairs, so the total sum is $-100$.
There are $200$ numbers on the list, so the average is $\frac{-100}{200} = -0.5$, and the answer is $\boxed{B}$