what is b in the following series. b, -3 , 4b, -12 if it is a G.P.

Given the series:

b, -3, 4b ,
-12 .

Let r be the common
difference.

Then we know
that:

-3 =
b*r................(1)

4b =
b*r^2.............(2)

-12 =
b*r^3.................(3)

First we will rewrite
(3).

-12 = br*r^2

But, from
(1), we know that  b*r = -3

==> -12 =
-3*r^2

==> r^2 = -12/-3 =
4

==> r1 = 2 ==> br= -3 ==> 2b=-3
==> b1= -3/2

==>
r2= -2 ==> br = -3 ==> -2b = -3 ==>  b2 =
3/2

==> -3/2, -3, -6 ,
-12  are terms of a G.P where r =
2

==> 3/2 , -3, 6,
-12    are terms of a G.P where r= -2