How do I work out the nth term?

The nth term falls into the topic of linear sequences.

A linear sequence is a set of numbers (such as "1, 2, 3, 4, ...") that are connected by a rule, which applies to every number in the sequence.

So, in the example of "1, 2, 3, 4, ...", the rule is to "Add 1" each time to get the next term.

To work out the nth term, we first must work out the common difference, and then we look at how we make the common difference equal one of the terms in the sequence. Usually, it will look something like 'n+1', or '3n-5'.

Example:
Work out the nth term for the linear sequence "2, 5, 8, 11, ...".

Step 1) We can see that the common difference is 3.

Can you see this? 5-2=3, 11-8=3 etc.

So, let's start by seeing if 3n works as a formula for the nth term:

When n=1, 3n=3, which is not a term in our sequence.

Step 2) If we subtract 1, we get 2, which is a term in our sequence.

Step 3) So, the nth term is "3n-1".

Let's check this: For n=3, 3n-1=9-1=8, which is our 3rd term.