If we KNOW there is a geometric sequence, division with any two consecutive values should produce the same result.
Let's try this one: 1, 2, 4, 6, 16
Notice: 2/1 = 2 and 4/2 = 2 and 8/4 = 2 and etc.
With your problem #1, we have:
I think it's wonderful that we used the common ratio to help solve for the missing variable value, but we did NOT yet solve for the common ratio.