Sequences · Year 11
In Year 11 you learn: geometric and Fibonacci-type sequences.
A sequence is a list of numbers that follows a rule, like 3, 7, 11, 15, … Once you know the rule you can predict any term — the next one or the 100th — without writing them all out.
Key facts
- Geometric sequences multiply by a common ratio r: 3, 6, 12, 24, …
- Quadratic sequences have a constant second difference; the coefficient of n² is half of it.
- Special sequences: square numbers 1, 4, 9, 16, …; triangular numbers 1, 3, 6, 10, …; Fibonacci 1, 1, 2, 3, 5, …
Worked examples
Example 1
Find the nth term of the quadratic sequence 3, 9, 17, 27, 39, …
Answer: n² + 3n − 1