AQA A Level Maths: Pure复习笔记4.5.1 Language of Sequences & Series

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

4.3.1-Lang-Seq-Ser-Illustr-1

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

4.3.1-Lang-Seq-Ser-Illustr-2

What is a series?

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

4.3.1-Lang-Seq-Ser-Illustr-3

  • We use the notation Sn to refer to the sum of the first n terms in the seriesie.   Sn = u1 + u2 + u3 + … + un

4.3.1-Lang-Seq-Ser-Illustr-4

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

4.3.1-Lang-Seq-Ser-Illustr-5

  • 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

4.3.1-Lang-Seq-Ser-Illustr-6

Exam Tip

Look out for sequences defined by trigonometric functions – this can be a way of 'hiding' a periodic function. 4.3.1-Lang-Seq-Ser-Illustr-7

Worked Example

4.3.1-Lang-Seq-Ser-Example

 

 

 

 

 

 

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