| Term | Definition | Example |
|---|---|---|
| Quadratic Sequence | A sequence where the second differences are constant | 2, 5, 10, 17, 26, 37... |
| First Differences | Differences between consecutive terms | 3, 5, 7, 9, 11... |
| Second Differences | Differences between first differences | 2, 2, 2, 2... |
| nth Term Formula | an² + bn + c | n² + 2n - 1 |
| Coefficient 'a' | Half of the second difference | If 2nd diff = 4, then a = 2 |
This key facts covers Key Facts within Quadratic Sequences for GCSE Mathematics. Revise Quadratic Sequences in Algebra for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 2 of 8 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Quadratic Sequences
Which of the following is a property of a quadratic sequence?
A student says: 'The sequence 3, 7, 13, 21, 31 is quadratic because the first differences increase.' Explain whether the student is correct and how to check properly.
Quick recall flashcards
What is a quadratic sequence?
A sequence where the second differences between consecutive terms are constant.
Example: 2, 5, 10, 17, 26, ...
First differences: 3, 5, 7, 9, ...
Second differences: 2, 2, 2, ... (constant)
What are second differences?
The differences between the first differences.
First differences: 4, 6, 8, 10
Second differences: 2, 2, 2
If second differences are constant, the sequence is quadratic.