Problem:
An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant to the previous term. For example, is an arithmetic sequence with five terms, in which the first term is and the constant added is . Each row and each column in this array is an arithmetic sequence with five terms. What is the value of
Answer Choices:
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Solution:
The middle number in an arithmetic sequence with terms is the average of the first and last numbers. The average of and is . The average of and is . Thus, is the average of and , or .
Alternatively, . In fact is the average of the four corner entries.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions