Number Patterns

What you'll learn

A number pattern (sequence) follows a rule; spotting the rule lets you find any term.

• A **sequence** is a list of numbers in order: \(2, 5, 8, 11, \ldots\)
• Each number is a **term**. The rule tells you how to get the next term.
• In \(2, 5, 8, 11\) the rule is **add 3** each time (a common difference of \(3\)).
• A sequence with a constant difference is **linear**; its \(n\)th term has the form \(an + b\).
• For \(2, 5, 8, 11\) the \(n\)th term is \(3n - 1\) (check: \(n = 1 \to 2\), \(n = 2 \to 5\)).