Edexcel IGCSE Maths

Revision Notes

3.1.1 Sequences - Basics

What are sequences?

  • A sequence is an order set of (usually) numbers
  • Each number in a sequence is called a term
  • The location of a term within a sequence is called its position
    • The letter n is often used for (an unknown) position
  • Subscript notation is used to talk about a particular term
    • a1 would be the first term in a sequence
    • a7 would be the seventh term
    • an would be the nth term

SeqBas Notes fig1, downloadable IGCSE & GCSE Maths revision notes

What is a position-to-term rule?

  • A position-to-term rule gives the nth term of a sequence in terms of n
    • This is a very powerful piece of mathematics
    • With a position-to-term rule the 100th term of a sequence can be found without having to know or work out the first 99 terms!

SeqBas Notes fig2, downloadable IGCSE & GCSE Maths revision notes

What is a term-to-term rule?

  • A term-to-term rule gives the (n+1)th term in terms of the nth term
    • ie an+1 is given in terms of an
    • If a term is known, the next one can be worked out

SeqBas Notes fig3, downloadable IGCSE & GCSE Maths revision notes

How do I use the position-to-term and term-to-term rules?

  • These can be used to generate a sequence
  • From a given sequence the rules can be deduced
  • Recognising and being aware of the types of sequences helps
    • Linear and quadratic sequences
    • Geometric sequences
    • Fibonacci sequences
    • Other sequences

SeqBas Notes fig4, downloadable IGCSE & GCSE Maths revision notes

Exam Tip

Write the position numbers above (or below) each term in a sequence.

This will make it much easier to recognise and spot common types of sequence.

SeqBas Example fig1 sola, downloadable IGCSE & GCSE Maths revision notes

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