top of page
A recurrence relation defines each term from previous terms, such as uₙ₊₁ = uₙ + d. This topic covers generating sequences from a recurrence, recognising periodic sequences and using sigma notation. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Each term is defined from the previous one. Substitute repeatedly to generate terms. For a periodic sequence, find the cycle length and use the remainder when dividing by it to jump to a distant term.
Before you start
Get sequences and substitution straight before you begin. Expect to use it again in modelling and periodic sequences.
What you learn
Sum one period, multiply, then add any spare terms. The toughest questions chain every idea in one go. The course works through generating terms, periodic sequences and order, sigma of a periodic sequence, sigma with an arithmetic or geometric adjustment, recurrence modelling and chained problems: periodic → sigma → adjustment. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Recurrence Relations is part of the Sequences & Series strand of our free A-level maths courses, studied in the AS year. It runs to 6 concepts, each followed by a check, with 6 worked examples along the way. It sits alongside Arithmetic Sequences, Arithmetic Series, Binomial Expansion (C12), Binomial Expansion (C34) and Geometric Sequences in the same strand. For unlimited practice, the Sequences & Series revision engine builds new questions on demand and records your accuracy.
Still need help with a topic?
bottom of page