Sequences · Grade 9
In Grade 9 you learn: quadratic sequences; 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
- Arithmetic sequences go up or down by a common difference d. Their nth term is dn + c.
- To find c, work out the “zero term”: the first term minus d.
- 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 5, 9, 13, 17, …
Answer: 4n + 1
Example 2
Is 150 a term of the sequence with nth term 7n − 4?
Answer: Yes, the 22nd term
Example 3
Find the nth term of the quadratic sequence 3, 9, 17, 27, 39, …
Answer: n² + 3n − 1