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

   

轉載自savemyexam