Problem:
Consider the sequence
1,−2,3,−4,5,−6,…,
whose nth term is (−1)n+1⋅n. What is the average of the first 200 terms of the sequence?
Answer Choices:
A. −1
B. −0.5
C. 0
D. 0.5
E. 1
Solution:
The 200 terms can be grouped into 100 odd-even pairs, each with a sum of −1. Thus the sum of the first 200 terms is −1⋅100=−100, and the average of the first 200 terms is −100/200=−0.5.