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