Posted by Lucas on Sunday, February 3, 2013 at 12:08pm.
a+d = ar
3/2 (2a+2d) = ar^2
3a+3d = ar^2
3(a+d) = ar^2
3ar = ar^2
3r = r^2
r = 3
So,
a+d = 3a
d = 2a
The sequences are thus
a,3a,5a,7a,9a,...
a,3a,9a,27a,...
Note that a+3a+5a = 9a, as required
Pick a value for a, and plug and chug.