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
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!
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
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
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.