Find x so that x−2,x+2 and x+4 are consecutive terms of a geometric sequence.
+23246 Geometric sequence: x - 2, x + 2, x + 4
Since this sequence is geometric, there is a value r such that:
r(x - 2) = x + 2 and r(x + 2) = x + 4
r = (x + 2) / (x - 2) r = (x + 4) / (x + 2)
Setting these two equal to each other: (x + 2) / (x - 2) = (x + 4) / (x + 2)
(x + 2)(x + 2) = (x - 2)(x + 4)
x2 + 4x + 4 = x2 + 2x - 8
2x = -12
x = -6
