Problem:
The first four terms of an arithmetic sequence are , and . What is the term of this sequence?
Answer Choices:
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Solution:
Consecutive terms in an arithmetic sequence have a common difference . Thus . Further, the second term is equal to , so , and the third term is equal to , so . These three equations form a system that can be solved to yield , and . Therefore the term of the sequence is .
The problems on this page are the property of the MAA's American Mathematics Competitions