a, a+d, a+2d forms AP that adds up to 24
ie. a + a+d + a+2d = 24
3a + 3d = 24
a + d = 8
a+1, a+d+1, a+2d+13 forms a GP
ie.
(a+d+1) / (a+1) = (a+2d+13) / (a+d+1)
expand and then use the relation that a+d = 8 to get everything in terms of a. You'll end up with a quadratic looking...