Finding Rules for Number Patterns

A number pattern such as \(4, 7, 10, 13, \ldots\) changes by the same step each time, and a rule describes every term at once. In NSW Year 8 maths, students turn patterns into tables and algebraic rules and use them to predict terms (NESA outcome MA4‑LIN‑C‑01).

You will continue increasing and decreasing patterns, find the rule linking \(x\) and \(y\) in a table of values, and write a rule for the \(n\)th term, such as \(T = 2n + 5\). You will use a rule to find a term far along the pattern, test whether a number belongs to it, and solve real problems about chairs around tables, stacked cups and weekly savings. A few patterns, like \(1, 1, 2, 3, 5, \ldots\), grow in other ways. It is part of Year 8 Graphing Linear Equations.