## What is a geometric sequence?

A geometric sequence is a sequence where the next term is found by multiplying the previous term by a number. Recursively, this can be expressed as: . The ratio of two successive terms is always the same . The explicit form of a geometric sequence is:

### Example of a geometric sequence

Consider the following geometric sequence:

To find the ratio , we have to divide on term by its previous term: . Indeed we can observe that every term in the sequence is found by multiplying the previous term by 3. The explicit form can be expressed as:

So to find the 5th element, for example, we substitute 5 for and get . We can confirm this because it is the same as the 5th element in the sequence shown above.