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). A first-order recurrence relation builds a sequence step by step, giving each term from the one just before it — for example \(u_n = 2u_{n-1}+3\) with \(u_1 = 1\).

Students and teachers will cover how to check an explicit formula for such a sequence and then prove it for all \(n\) by mathematical induction, using the recurrence to move from one term to the next — a careful blend of algebra and proof in the HSC Extension 2 course.