# How do you find the general term for a sequence?

##### 1 Answer

It depends.

#### Explanation:

There are many types of sequences. Some of the interesting ones can be found at the online encyclopedia of integer sequences at https://oeis.org/

Let's look at some simple types:

e.g.

There is a common difference between each pair of terms.

If you find a common difference between each pair of terms, then you can determine

e.g.

There is a common ratio between each pair of terms.

If you find a common ratio between pairs of terms, then you have a geometric sequence and you should be able to determine

**Iterative Sequences**

After the initial term or two, the following terms are defined in terms of the preceding ones.

e.g. Fibonacci

For this sequence we find:

There are many ways to make these iterative rules, so there is no universal method to provide an expression for

**Polynomial Sequences**

If the terms of a sequence are given by a polynomial, then given the first few terms of the sequence you can find the polynomial.

e.g.

Form the sequence of differences of these values:

Form the sequence of differences of these values:

Once you reach a constant sequence like this, pick out the initial terms from each sequence. In this case

These form the coefficients of a polynomial expression: