2005 Pascal Problem 10

In the sequence 32, 8, \_\_\_ , \_\_\_, x, each term after the second is the average of the two terms immediately before it. The value of x is

\textbf{(A)}\ 17\quad \textbf{(B)}\ 20\quad \textbf{(C)}\ 44\quad \textbf{(D)}\ 24\quad \textbf{(E)}\ 14

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.