The numbers a, b, c and d form a geometric sequence, in that order. If b is 3 more than a, and c is 9 more than b, what is the value of d? Express your answer as a mixed number.
a * r = a +3
a * r * r = a+3 + 9
(a+3) * r = a + 12
r = (a+12)/(a+3)
a ( a+12)/(a+3) = a + 3
a^2 + 12a = a^2 +6a + 9
6a = 9
a = 3/2
3/2 * r = 3/2 + 3
r = 9/2 * 2/3 = 3
a b c d
So the sequence is 3/2 9/2 27/2 81/2 d = 40 1/2