For real numbers $a, b$ and $c$ we have \[(2b-a)^2 + (2b-c)^2 = 2(2b^2-ac).\] Prove that the numbers $a, b$ and $c$ are three consecutive terms in some arithmetic sequence.
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Tags: arithmetic sequence, algebra proposed, algebra
For real numbers $a, b$ and $c$ we have \[(2b-a)^2 + (2b-c)^2 = 2(2b^2-ac).\] Prove that the numbers $a, b$ and $c$ are three consecutive terms in some arithmetic sequence.