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Recurrence relation worksheet
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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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.
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