What's the common ratio for 4, 12, 36, 108, ... ?

The term common ratio in this question refers to the number which is the ratio between two numbers of a geometric sequence. 

There are two ways of finding the common ratio of a geometric sequence: (1) The first one is to divide the number and the number after it. That is, in this question we have:

4, as the first number and 12 the number after it. Then, 12/4 = 3. The same also with 12 and 36, that is 36/12 = 3. Therefore, the common ratio is 3.

(2) Now, we go the next method of finding the common ratio of a geometric sequence which is by the use of the formula in geometric sequence. The formula is:

`t=ar^(n-1)`

By the formula, we determine first the first term a, which is 4, the last term t, which is 108 and the number n which is the number of the last term in the sequence. Then, we solve for the ratio.

`108=4r^(4-1)` 

`108=4r^(3)`  divide both sides by 4, we have

`27=r^(3)` Get the cube root of each side, it will become

`root(3)(27)=root(3)(r^(3))`  and finally, we have

3=r or simply r=3.

Therefore, the common ratio is 3.