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A LevelMaths: PureOCRRevision Notes4. Sequences and Series4.5 Sequences & Series4.5.1 Language of Sequences & Series

Language of Sequences & Series (OCR A Level Maths: Pure)

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Roger

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Language of Sequences & Series

What is a sequence?

  • A sequence is an ordered set of numbers with a rule for finding all the numbers in the sequence

Lang Seq Ser Illustr 1, A Level & AS Level Pure Maths Revision Notes 

  • The numbers in a sequence are called terms
  • The terms of a sequence are often referred to by letters with a subscript

 Lang Seq Ser Illustr 2, A Level & AS Level Pure Maths Revision Notes

 

What is a series?

  • You get a series by summing up the terms in a sequence

Lang Seq Ser Illustr 3, A Level & AS Level Pure Maths Revision Notes 

  • We use the notation Sn to refer to the sum of the first n terms in the series

    ie.   Sn = u1 + u2 + u3 + … + un

Lang Seq Ser Illustr 4, A Level & AS Level Pure Maths Revision Notes

Increasing, decreasing and periodic sequences

  • A sequence is increasing if un+1 > un for all positive integers n – ie if every term is greater than the term before it
  • A sequence is decreasing if un+1 < un for all positive integers n – ie if every term is less than the term before it

Lang Seq Ser Illustr 5, A Level & AS Level Pure Maths Revision Notes

  • A sequence is periodic if the terms repeat in a cycle
  • The order (or period) of a periodic sequence is the number of terms in each repeating cycle

Lang Seq Ser Illustr 6, A Level & AS Level Pure Maths Revision Notes

Examiner Tip

Look out for sequences defined by trigonometric functions – this can be a way of 'hiding' a periodic function. Lang-Seq-Ser-Illustr-7, A Level & AS Level Pure Maths Revision Notes

Worked example

Lang Seq Ser 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.