Question

Insert the geometric means.
-1,_,-125,_,-3125

Answer 1

sorry, you don't have a constant ratio
125/1 ≠ 3125/125

However, the sequence could have r=±5, if the first term were -5 instead of -1.

Answer 2

x^2 = (-1)(-125) = 125
x = ±5√5

since -1 is your first term, ±5√5 also becomes the r value .

y^2 = (-125)(-3125) = 390625
y = √390625 = 625

your GP
if r = +√125
the sequence is -1, -√125, - 125, -125√125, - 15625
if r = -5√5
the sequence is -1, +√125, - 125, +125√125, - 15625

something is wrong here.
I was expecting -3125 , as was stated in your problem
If a, b, c, form a geometric sequence,
then b^2 = ac, that is the square of any term must equal the product
of the terms on either side of it