Question

Insert five geometric means between 0.125 and 8.



I know one set is 0.25, 0.5, 1, 2, 4

What would be the other set?

Answer 1

I think you have the answer. The question said 5 means and didn't say 5 different sets of means. I can't think of another way that you can get from .125 to 8.

Answer 2

.125 , .125r, .125r^2, .125r^3, .125r^4, .125r^5, 8

.125r/.125 = 8/.125r^5

r = 64/r^5
r^6 = 64
r = ± 2

set 1:
.25, .5, 1, 2, 4

set 2: if r = -2
-.25, .5, -1, 2, -4

Answer 3

Write the geometric sequence that has five geometric means between 1and 15,625.

1, 5, 20, 125, 615, 3,125, 15,625, …

1, 5, 25, 125, 625, 3,125, 15,625, …

1, 5, 25, 125, 620, 3,250, 15,625, …

1, 5, 25, 125, 652, 3,350, 15,625, …