Edexcel IGCSE Maths 复习笔记 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
  • a_n would be the n^th term

   

What is a position-to-term rule?

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

   

What is a term-to-term rule?

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

   

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

   

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