Difficulty: Medium Easy
SMP-CCSS: 1. Make sense of problems and persevere in solving them; 4. Model with mathematice
CCSS-M: 7.RP.A. Analyze proportional relationships and use them to solve real-world and mathematical
3
AMC 8 Practice Questions Continued
13-03
What is the value of $4 \cdot(-1+2-3+4-5+6-7+\cdots+1000) ?$
(A) -10
(B) 0
(C) 1
(D) 500
(E) 2000
Answer
Final Answer: \(\boxed{2000}\)
Step 1 ：The given expression is a series of numbers from -1 to 1000 with alternating signs. We can observe that the series can be grouped into pairs of two numbers, where the first number is negative and the second number is positive. For example, \((-1+2)\), \((-3+4)\), \((-5+6)\), and so on. Each pair sums up to 1.
Step 2 ：Since there are 500 pairs (1000 numbers divided by 2), the sum of the series is 500.
Step 3 ：Multiplying this sum by 4 gives the final answer: \(500 \times 4 = 2000\).
Step 4 ：Final Answer: \(\boxed{2000}\)
