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