2003 AMC 10B Problem 24

The first four terms in an arithmetic sequence are x + y, x - y, xy, and x/y, in that order. What is the fifth term?

\textbf{(A)}\ -\frac{15}{8}\qquad\textbf{(B)}\ -\frac{6}{5}\qquad\textbf{(C)}\ 0\qquad\textbf{(D)}\ \frac{27}{20}\qquad\textbf{(E)}\ \frac{123}{40}

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