# Recurrence relation worksheet • Section 1 of the recurrence relation worksheet contains 36 skills-based recurrence relation questions, in 3 groups to support differentiation
• Section 2 contains 5 applied recurrence relation questions with a mix of worded problems and deeper problem solving questions
• Section 3 contains 3 foundation and higher level GCSE exam style recurrence relation questions
• Answers and a mark scheme for all recurrence relation questions are provided
• Questions follow variation theory with plenty of opportunities for students to work independently at their own level
• All questions created by fully qualified expert secondary maths teachers
• Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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### Recurrence relation at a glance

A recurrence relation is a relation which creates a sequence of numbers. Consecutive terms of a sequence are found using a rule which gives the next term based on the current term. An example of a linear recurrence relation is u_{n+1}=2u_{n}+3. If the first term is 5, the next terms of the sequence  are found by multiplying each previous term by 2 and then adding 3.

u_{0}=5

u_{1}=2×5+3=13

u_{2}=2×13+3=29 etc. . .

We might be asked to find an expression for u_{n}. This is the nth term formula for the sequence. A recurrence relation of the form u_{n+1}=u_{n}+a where the coefficient of u_{n} is 1 and a is a constant, will produce a linear sequence. An example of this is the following recurrence relation: u_{n+1}=u_{n}+5 with initial value u_{0}=1, which gives the following sequence: 1, 6, 11, 16, 21, …. In this case, we can find u_{n}=5n-4.

Looking forward, students can then progress to additional sequences worksheets or more  algebra worksheets, for example a sequences worksheet, or simultaneous equations worksheet. For more teaching and learning support on Algebra our GCSE maths lessons provide step by step support for all GCSE maths concepts.

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