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A LevelMaths: Pure 1CIERevision Notes4. Sequences & Series4.4 Further Sequences & Series4.4.1 Language of Sequences & Series

Language of Sequences & Series (CIE A Level Maths: Pure 1)

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Language of Sequences & Series

What is a progression/sequence?

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

 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 progression 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 progression

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 progression

    ie.   Sn = u1 + u2 + u3 + … + un

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

Increasing, decreasing and periodic progressions

  • A progression is increasing if un+1 > un for all positive integers n – ie if every term is greater than the term before it
  • A progression 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 progression is periodic if the terms repeat in a cycle
  • The order (or period) of a periodic progression 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 progressions 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.