Find x so that x-2, x+2 and x+4 are consecutive terms of a geometric sequence.
Call the common ratio , r
(x - 2)r = ( x + 2) ⇒ xr - 2r = x + 2 (1)
( x +2)r = x + 4 ⇒ xr + 2r = x + 4 (2)
Subtract (1) from (2)
4r = 2
r = 2/4 = 1/2
Using the first equation
x (1/2) - 2(1/2) = x + 2
(1/2)x - 1 = x + 2
-(1/2)x = 3
x = 3/(-1/2) = -6
(x - 2) = -8
( x + 2) = -4
(x + 4) = -2