Sequences

In a Nutshell

A sequence is a list of numbers that follows a rule — spot the pattern and you can predict what comes next.

A sequence is an ordered list of numbers called terms. Each term has a position: the first term, the second term, and so on. To continue a sequence you need to find the rule that connects one term to the next.

The simplest type is an arithmetic sequence (also called a linear sequence). Here, you add (or subtract) the same amount each time. That fixed amount is the common difference.

For example, in $2,; 5,; 8,; 11,; 14,; \\$ the common difference is $+3$ because each term is 3 more than the one before.

First term Common difference

Change the first term and common difference to explore different sequences. Watch how the arrows between terms always show the same step.

Watch it work

Question: Find the next two terms of the sequence $7,; 12,; 17,; 22,; \\$

Have a go

Q1. Find the next two terms: $4,; 9,; 14,; 19,; \\$

Q2. Find the next two terms: $20,; 17,; 14,; 11,; \\$

Q3. Find the common difference and the next term: $1,; 4,; 7,; 10,; \\$

Q4. Write the first five terms of a sequence that starts at $2$ and has a common difference of $6$ .