IBMathsDPApplications & Interpretation (AI)SLRevision Notes1. Number & AlgebraSequences & SeriesLanguage of Sequences & Series

Language of Sequences & Series (DP IB Applications & Interpretation (AI)): Revision Note

Amber

Written by: Amber

Reviewed by: Mark Curtis

Updated on

DP Applications & Interpretation (AI): SLDP Applications & Interpretation (AI): HLDP Analysis & Approaches (AA): HLDP Analysis & Approaches (AA): SLDP Analysis & Approaches (AA): HLDP Analysis & Approaches (AA): SLDP Applications & Interpretation (AI): HLDP Applications & Interpretation (AI): SL

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 the letter u with a subscript

      • So in the sequence above, u subscript 1 equals 1 comma space u subscript 2 equals 3 comma space u subscript 3 equals 5 comma space...

      • The nth term is u subscript n

  • If a formula for the nth term is given, then each term in the sequence can be found by substituting the term number, n, into the formula

    • e.g. if u subscript n equals 2 n minus 1then the 5th term is u subscript 5 equals 2 cross times 5 minus 1 equals 9

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 +  …

  • The notation S subscript n is used to refer to the sum of the first n terms in a series

    • S subscript n equals u subscript 1 plus u subscript 2 plus u subscript 3 plus... u subscript n

    • For the series above, S subscript 4 equals 1 plus 3 plus 5 plus 7 equals 16

Worked Example

Determine the first five terms and the value of S subscript 5 in the sequence given by u subscript n equals 5 minus 2 n.

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

You've read 1 of your 5 free revision notes this week

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

  • I would just like to say a massive thank you for putting together such a brilliant, easy to use website.I really think using this site helped me secure my top gradesin science and maths. You really did save my exams! Thank you.

    Beth
    IGCSE Student

  • This website is soooo useful and I can’t ever thank you enough for organising questions by topic like this. Furthermore, the name of the website could not have been more appropriate as it literally did SAVE MY EXAMS!

    Fathima
    A Level Student
Test yourselfFlashcards

Did this page help you?

Previous:Solving Equations using a GDCNext:Sigma Notation
Author
Reviewer
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.

Mark Curtis

Reviewer: Mark Curtis

Expertise: Maths Content Creator

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

Download notes on Language of Sequences & Series