AMC 12 2004a Problem 14

A sequence of three real numbers forms an arithmetic progression with a first term of $9$. If $2$ is added to the second term and $20$ is added to the third term, the three resulting numbers form a geometric progression. What is the smallest possible value for the third term in the geometric progression?

$\text {(A) } 1 \text {(B) } 4 \text {(C) } 36 \text {(D) } 49 \text {(E) }81$