AHSME 1980 Problem 11

If the sum of the first $10$ terms and the sum of the first $100$ terms of a given arithmetic progression are $100$ and $10$, respectively, then the sum of first $110$ terms is: $\text{(A)} \ 90 \text{(B)} \ -90 \text{(C)} \ 110 \text{(D)} \ -110 \text{(E)} \ -100$