Problem:
In the five-sided star shown, the letters , and are replaced by the numbers , and , although not necessarily in this order. The sums of the numbers at the ends of the line segments , and form an arithmetic sequence, although not necessarily in this order. What is the middle term of the arithmetic sequence?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Each number appears in two sums, so the sum of the sequence is
The middle term of a five-term arithmetic sequence is the mean of its terms, so is the middle term.
The figure shows an arrangement of the five numbers that meets the requirement.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions