Language of Sequences & Series (DP IB Analysis & Approaches (AA)): Revision Note

Did this video help you?

Language of Sequences & Series

What is a sequence?

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

    • For example 1, 3, 5, 7, 9, … is a sequence with the rule ‘start at one and add two to each number’

  • The numbers in a sequence are often called terms

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

    • In IB this will be the letter u

    • So in the sequence above, u1 = 1, u2 = 3, u3 = 5 and so on

  • Each term in a sequence can be found by substituting the term number into formula for the nth term

     

What is a series?

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

    • E.g. For the sequence 1, 3, 5, 7, … the associated series is 1 + 3 + 5 + 7 +  …

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

    • Sn = u1 + u2 + u3 + … + un

    • So for the series above S5 = 1 + 3 + 5 + 7 + 9 = 25

Worked Example

Determine the first five terms and the value of S5 in the sequence with terms defined by un  = 5 - 2n.

ai-sl-1-2-1-language-we-so

Did this video help you?

Sigma Notation

What is sigma notation?

  • Sigma notation is used to show the sum of a certain number of terms in a sequence

  • The symbol Σ is the capital Greek letter sigma

  • Σ stands for ‘sum’

    • The expression to the right of the Σ tells you what is being summed, and the limits above and below tell you which terms you are summing

4-5-2-sigma-not-illustr-1
  • Be careful, the limits don’t have to start with 1

    • For example sum from k space equals space 0 to 4 of left parenthesis 2 k plus 1 right parenthesis  or  sum from k space equals space 7 to 14 of left parenthesis 2 k minus 13 right parenthesis

    • r and k are commonly used variables within sigma notation

Examiner Tips and Tricks

  • Your GDC will be able to use sigma notation, familiarise yourself with it and practice using it to check your work

Worked Example

A sequence can be defined by  u subscript n equals space 2 space cross times space 3 to the power of n minus 1 end exponent for  n element of space straight integer numbers to the power of plus .

 

a) Write an expression for u subscript 1 space plus space u subscript 2 space plus space u subscript 3 space plus space... space plus space u subscript 6 using sigma notation.

ai-sl-1-2-1-sigma-a

 

b) Write an expression for u subscript 7 space plus space u subscript 8 space plus space u subscript 9 space plus space... space plus space u subscript 12using sigma notation.

ai-sl-1-2-1-sigma-b
👀 You've read 1 of your 5 free revision notes this week
An illustration of students holding their exam resultsUnlock more revision notes. It's free!

By signing up you agree to our Terms and Privacy Policy.

Already have an account? Log in

Did this page help you?

Amber

Author: Amber

Expertise: Maths Content Creator

Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

Download notes on Language of Sequences & Series