1997 AHSME Problem 14

The number of geese in a flock increases so that the difference between the populations in year n+2 and year n is directly proportional to the population in year n+1. If the populations in the years 1994, 1995, and 1997 were 39, 60, and 123, respectively, then the population in 1996 was

\textbf{(A)}\ 81\qquad\textbf{(B)}\ 84\qquad\textbf{(C)}\ 87\qquad\textbf{(D)}\ 90\qquad\textbf{(E)}\ 102

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