AMC 12 2002b 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

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