Insert the geometric means.
1,_,125,_,3125
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2 answers

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. 👍
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oobleck 
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 👍
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