Algebra

Let x be the constant that is added to all 3 numbers, and let d be the common ratio

We have: $(60+x)d = (100 + x)$

Solving for d gives us: $d = {100 + x \over 60 + x }$

We also know from the second and final term that $(100 + x) d = (180 + x)$

Substituting the known value of d, we have: $(100 + x) \times {100 + x \over 60 + x} = (180 + x)$

Cross multiplying gives: $(x + 100)^2 = (180 + x)(60 + x)$

Simplify both sides to: $x^2+200x+10000=x^2+240x+10800$

Solving for x gives us: $x = -20$

This means that the geometric series is $40, 80, 160$. 

Can you find the common ratio from here?

The common ratio is 11/3.