The numbers 4x,2x−3,4x−3 are three consecutive terms in an arithmetic sequence. What is the value of x?
(An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, 3,5,7,9 are the first four terms of an arithmetic sequence.)
Pick one
Solution
Since 4x,2x−3,4x−3 form an arithmetic sequence, then the differences between consecutive terms are equal, or (2x−3)−4x=(4x−3)−(2x−3).
Thus, −2x−3=2x or 4x=−3 and so x=−43.
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