Problem:
In the five-sided star shown, the letters and are replaced by the numbers and 9 , although not necessarily in that order. The sums of the numbers at the ends of the line segments and form an arithmetic sequence, although not necessarily in that 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.
The problems on this page are the property of the MAA's American Mathematics Competitions