nth term

Remember that a sequence has some key features:
  • each number in a sequence is called a term
  • each term has a position, eg 1st, 2nd, 3rd etc
  • the terms are linked by a pattern or rule
  • in arithmetic (or linear) sequences the rule is to add or subtract a common difference

Finding the nth term

1, 4, 7, 10... is a sequence starting with 1.

The 1st term is 1, the 2nd term is 4, the 3rd term is 7 etc.

You get the next term by adding three to the previous term. The rule is + 3.

So you can find any term if you know the previous term. But how do you find the term for any position without working out all the terms that come before it?

We use the nth term to stand for any term where n is its position.

To find the nth term of a sequence, you first work out the formula of the sequence.

In maths you are often asked to find the formula for the nth term of a sequence.