# How do find the #n#th term in a sequence?

##### 1 Answer

It depends on the type of sequence.

If the sequence is an arithmetic progression with first term

for some constant b.

If the sequence is a geometric progression with first term

for some constant

There are also sequences where the next number is defined iteratively in terms of the previous 2 or more terms. An example of this would be the Fibonacci sequence:

Each term is the sum of the two previous terms.

The ratio of successive pairs of terms tends towards the golden ratio

The terms of the Fibonacci sequence are expressible by the formula:

In general an infinite sequence is any mapping from

Finite sequences are the same, except that they are mappings from a finite subset of