In this mathematics lesson students learn how to generate terms of a sequence using a recurrence formula. As learning progresses they consider second term sequences as well as deriving possible formulae from a pattern. The start of the lesson is used to recap the difference between geometric and arithmetic sequences by categorising various patterns into each group.

### Differentiated Learning Objectives

- All students should be able to generate the first six terms of a recurrence sequence in the form U
_{n+1} = aU_{n} + c - Most students should be able to generate the first six terms of a recurrence sequence using the previous term.
- Some students should be able to generate the first six terms of a recurrence sequence in the form U
_{n+2} = aU_{n+1} + cU_{n}

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