How do I find the common ratio of .$\dots ,4, \text{ __ }, \text{ __ },108$?

Question

How can I find the common ratio of $\dots ,4, \text{ __ }, \text{ __ },108$? And find the missing terms? I tried doing it and I got $3$ for the common ration but for some reason my friend said my common ration was wrong, so please can anybody help me?

Answer 1

Hint: Consider $$ 2^2, 3\cdot 2^2, 3^2\cdot 2^2,3^3\cdot 2^2. $$

Answer 2

HINT

I think the idea is you have 4 elements with common ratio: $4,x,y,108$. Let's say the common ratio is $r$. Then, $x = 4r$ and $y = xr = (4r)\cdot r = 4r^2$. Can you express $108$ in terms of $r$ and solve to find $r$?