Nth Term Sequences

The { n }^{ th } term is a rule consisting of the variable, n, which enables you to find any term of the sequence without having to go through each one.

We work out the { n }^{ th } term by finding

If I am trying to find the 67th term of a sequence, I would first generate the rule of the sequence, which we call the { n }^{ th } term and then substitute 67 into n.

Example

If we pick a sequence from above, consisting of the following numbers: 2,4,6,8,10,…

We are able to work out that the { n }^{ th } term is 2n.

In order to find the 23rd term of the sequence, we substitute 23 for n:\quad 2\times 23=46.

Therefore, the 23^rd term of the sequence is 46.