Problem:
Consider the sequence
1,β2,3,β4,5,β6,β¦,
whose nth term is (β1)n+1β
n. What is the average of the first 200 terms of the sequence?
Answer Choices:
A. β1
B. β0.5
C. 0
D. 0.5
E. 1
Solution:
The 200 terms can be grouped into 100 odd-even pairs, each with a sum of β1. Thus the sum of the first 200 terms is β1β
100=β100, and the average of the first 200 terms is β100/200=β0.5.