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**Help your students prepare for their Maths GCSE with this free ****recurrence relation** **worksheet** **of 44 questions and answers**

- 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
- Free downloadable and printable resources

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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.

There will be students in your class who require individual attention to help them succeed in their maths GCSEs. In a class of 30, it’s not always easy to provide.

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Lessons are selected to provide support where each student needs it most, and specially-trained GCSE maths tutors adapt the pitch and pace of each lesson. This ensures a personalised revision programme that raises grades and boosts confidence.