Answer
$$\require{cancel}
\\\sum_{k=1}^{24}-k=-300$$
Work Step by Step
RECALL:
(1) $$\sum_{i=1}^{n}k = \dfrac{n(n+1)}{2}$$
(2) $$\sum_{i=1}^{n}-k = -\sum_{k=1}^{n}k$$
Use rule (2) above to obtain:
$$\sum_{k=1}^{24}(-k) = -\sum_{k=1}^{24}k$$
Use rule (1) above to obtain:
$$\require{cancel}
\\-\sum_{k=1}^{24}k=-\dfrac{24(25)}{2}=-300$$