This exam tips covers Top Tips 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 7 of 8 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.
Top Tips
- Recognition: If first differences are not constant but second differences are, it's quadratic
- Always check: Substitute values back into your formula to verify it works
- Common mistake: Forgetting that a = ½ × (second difference), not the full second difference
- Pattern tip: Quadratic sequences often involve square numbers, triangular numbers, or growth patterns
- Real-world: Look for quadratic sequences in physics (distance = ½at²), economics (compound interest), and geometry (areas)
- Negative 'a': When a < 0, the sequence eventually decreases (like throwing a ball up)
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 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.
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)