2004 AMC 12A 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 \qquad \text {(B) } 4 \qquad \text {(C) } 36 \qquad \text {(D) } 49 \qquad \text {(E) }81

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.