ANSWER
12, 36, 108 and 324.
EXPLANATION
We want to find 4 geometric means between 4 and 972.
Let w, x, y and z be the four geometric means.
So, we have that:
4, w, x, y, z, 972
The first term, a, of this progression is 4.
The 6th term is 972
We have that the nth term of a geometric progression is:
Let us find r by using the 6th term:
Now, let us find the four terms:
=> w is the second term, so n = 2:
=> x is the thrid term, so n = 3:
=> y is the fourth term, so, n = 4:
=> z is the fifth term, so n =5:
So, the four geometric means are 12, 36, 108 and 324.