AMC 12 2014a Problem 14

Let $a<b<c$ be three integers such that $a,b,c$ is an arithmetic progression and $a,c,b$ is a geometric progression. What is the smallest possible value of $c$?

$\textbf{(A) }-2 \textbf{(B) }1 \textbf{(C) }2 \textbf{(D) }4 \textbf{(E) }6$