Question

What is the value of $\begin{aligned} &4 \cdot (-1 + 2 - 3 + 4 - 5 + 6 \\ &\qquad {}- 7 + \cdots + 1000)? \end{aligned}$

$-10$

$0$

$1$

$500$

$2000$

Click to load, then click again to play

Within the parentheses, pair consecutive terms: $\begin{aligned} &(-1+2)+(-3+4) \\ &\quad {}+\cdots+(-999+1000). \end{aligned}$

Each pair has sum $1$ , and there are $500$ pairs, so the value inside the parentheses is $500$ . Multiplying by $4$ gives $2000$ .

Thus, E is the correct answer.