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Arithmetic and Geometric Series

Source: 2014 AMC 12A #14

February 5, 2014
ratioarithmetic sequencegeometric seriesAMC

Problem Statement

Let a<b<ca<b<c be three integers such that a,b,ca,b,c is an arithmetic progression and a,c,ba,c,b is a geometric progression. What is the smallest possible value of cc?
<spanclass=′latex−bold′>(A)</span>−2<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>4<spanclass=′latex−bold′>(E)</span>6<span class='latex-bold'>(A) </span>-2\qquad <span class='latex-bold'>(B) </span>1\qquad <span class='latex-bold'>(C) </span>2\qquad <span class='latex-bold'>(D) </span>4\qquad <span class='latex-bold'>(E) </span>6\qquad
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