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

Hello!

A common ratio is a term which applies to a geometric sequence. A geometric sequence starts from any number `a` and any next term is equal to the previous term multiplied by a fixed number `r.` This number `r` is called the common ratio of a geometric sequence.

Consider the given sequence. It starts from the number 4. The next number is 12/4=3 times greater than the first. So if this sequence is a...

Hello!

A common ratio is a term which applies to a geometric sequence. A geometric sequence starts from any number `a` and any next term is equal to the previous term multiplied by a fixed number `r.` This number `r` is called the common ratio of a geometric sequence.

Consider the given sequence. It starts from the number 4. The next number is 12/4=3 times greater than the first. So if this sequence is a geometric one, then the next term must be 12*3=36. This is true, and the next term must be 36*3=108, which is also true.

Therefore this sequence is a geometric one and its common ratio is 3. We can predict its next terms: 108*3=324, 324*3=972 and so on. The n-th term is

`a_n=4*3^(n-1).`