Question

insert 3 geometric means between 1 and 256.

Answer 1

Let the geometric means be
a=1,ar,ar2,ar3,ar4 = 256
you get, r4=256
r = 4
Geometric Means are 4,16,64

Answer 2

A_1 = 256
a_5 = 1

a_n = (a_1)[r^(n - 1)]
1 = 256[r^5 - 1)]
1/256 = r^4
+- 1/4 = r


If r = 1/4

256, 64, 16, 4, 1

If r = -1/4

256, -64, 16, -4, 1