ASMaths: Pure 1CIERevision Notes4. Sequences & Series4.4 Further Sequences & Series4.4.3 Recurrence Relations

Recurrence Relations (CIE AS Maths: Pure 1)

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Recurrence Relations

What do I need to know about recurrence relations?

  • A recurrence relation describes each term in a progression 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

 

Recur Rel Illustr 1, A Level & AS Level Pure Maths Revision Notes

 

  • Both arithmetic progressions and geometric progressions can be defined using recurrence relations
    • Arithmetic can be defined by u subscript n plus 1 end subscript equals u subscript n plus d comma space u subscript 1 equals a
    • Geometric can be defined by u subscript n plus 1 end subscript equals u subscript n cross times r comma space u subscript 1 equals a

 

Recur Rel Illustr 2, A Level & AS Level Pure Maths Revision Notes

 

  • However, you can also define progressions that are neither arithmetic nor geometric

 

Recur Rel Illustr 3, A Level & AS Level Pure Maths Revision Notes

Examiner Tip

  • For arithmetic or geometric progressions defined by recurrence relations, you can sum the terms using the arithmetic series and geometric formulae.
  • To sum up the terms of other progressions, you may have to think about the series and find a clever trick.

Worked example

Recur Rel Example, A Level & AS Level Pure Maths Revision Notes

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    Roger

    Author: Roger

    Expertise: Maths

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.