Find x so that x + 6, x + 12 and x + 15 are consecutive terms of a Geometric Progression.

Find x so that x + 6, x + 12 and x + 15 are consecutive terms of a Geometric Progression.
Solution :
b  = √ac
(x + 12)  = √(x + 6) (x + 15)
Taking squares on both sides,
(x + 12)2  = (x + 6) (x + 15)
x2 + 122 + 2x(12)  = x2 + 15x + 6x + 90
144 + 24x  = 21x + 90
24x - 21x  = 90 - 144
3x  = -54
x  = -18

Hence the value of x is -18.