2002 AMC 12B Problem 9

If a,b,c,d are positive real numbers such that a,b,c,d form an increasing arithmetic sequence and a,b,d form a geometric sequence, then \frac ad is

\mathrm{(A)}\ \frac 1{12} \qquad\mathrm{(B)}\ \frac 16 \qquad\mathrm{(C)}\ \frac 14 \qquad\mathrm{(D)}\ \frac 13 \qquad\mathrm{(E)}\ \frac 12

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