Induction – Recursive (first-order recurrence)

Proof by mathematical induction for recursive formulas is part of the Proof topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-01). This subtopic explains that a recursive formula, or recurrence relation, defines each term of a sequence from a preceding term, then uses induction to prove a general result for such a sequence.

Students and teachers will cover how to prove results involving first-order recurrence relations by mathematical induction — connecting a recursively defined sequence to an explicit formula, a skill assessed in the HSC Extension 2 course.