Sequence - GCSE Maths Definition

A sequence is a set of numbers that follow a specific order or pattern. Each number in a sequence is called a term.

Sequences can be defined by a term-to-term rule, or a position-to-term rule (n^th formula).

For example, in the sequence 5, 9, 13, 17, ... the term-to-term rule is "add 4"; the position-to-term rule is "multiply the position by 4, then add 1" (written mathematically, as the n^th term formula, this would be ).

There are various types of sequence that can occur, and you already know some particular number sequences (and not just odd and even numbers!). Examples are

• an arithmetic sequence is where here is a constant difference between consecutive terms - i.e. the sequence either increases or decreases by a constant amount from one term to the next

• a geometric sequence is where is a (constant) multiplier between consecutive terms - i.e. the term-to-term rule is to multiply by <a number>

• the Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, ... - each term is the sum of the previous two; this sequence occurs a lot in nature

• the square numbers - 1, 4, 9, 16, 25, ...