Evaluate $(-50)+(-48)+(-46)+\ldots+54+56$.
(A) 156
(B) 10
(C) 56
(D) 110
(E) 162
Evaluate $(-50)+(-48)+(-46)+\ldots+54+56$.
(A) 156
(B) 10
(C) 56
(D) 110
(E) 162

## Solution

If we add some terms to this series, we would have the following:

$$
(-50)+(-48)+(-46)+\ldots+48+50+52+54+56
$$

Each of the negative integers has its opposite included in the sum and each pair of these sums is 0 .

This implies that, $(-50)+(-48)+(-46)+\ldots+46+48+50$ is 0 . The overall sum is now just $52+54+56$ or 162 .

ANSWER: (E)