# What is the common ratio of the geometric sequence 2, 6, 18, 54,...?

##### 1 Answer

Feb 3, 2015

A geometric sequence has a common ratio, that is: the divider between any two nextdoor numbers:

You will see that

Or in other words, we multiply by

So we can predict that the next number will be

If we call the first number

**In general**

The

**Extra:**

In most systems the 1st term is not counted in and called term-0.

The first 'real' term is the one after the first multiplication.

This changes the formula to

(which is, in reality, the (n+1)th term).