Problem:
Suppose that Suppose that {an} is an arithmetic sequence with
a1+a2+⋯+a100=100
and
a101+a102+⋯+a200=200
What is the value of a2−a1?
Answer Choices:
A. 0.0001
B. 0.001
C. 0.01
D. 0.1
E. 1
Solution:
Let d=a2−a1. Then ak+100=ak+100d, and
a101+a102+⋯+a200=(a1+100d)+(a2+100d)+…+(a100+100d)=a1+a2+…+a100+10,000d
Thus 200=100+10,000d and d=10,000100=0.01.
Answer: C.
The problems on this page are the property of the MAA's American Mathematics Competitions