Edexcel A Level Maths: Pure:复习笔记4.5.3 Recurrence Relations
Recurrence Relations
What do I need to know about recurrence relations?
- A recurrence relation describes each term in a sequence as a function of the previous term – ie un+1 = f(un)
- Along with the first term of the sequence, this allows you to generate the sequence term by term
- Both arithmetic sequences and geometric sequences can be defined using recurrence relations
- Arithmetic can be defined by
- Geometric can be defined by
- Arithmetic can be defined by
- However, you can also define sequences that are neither arithmetic nor geometric
Exam Tip
- For arithmetic or geometric sequences defined by recurrence relations, you can sum the terms using the arithmetic series and geometric series formulae.
- To sum up the terms of other sequences, you may have to think about the series and find a clever trick.
Worked Example
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