AQA 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
    • 4.3.3-Recur-Rel-Illustr-2
  • 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