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Quadratic Sequence Structure

Part of Quadratic Sequences — GCSE Mathematics

This diagram covers Quadratic Sequence Structure 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 3 of 7 in this topic. Focus on the labels, the relationships between parts, and the explanation that turns the diagram into an exam-ready answer.

Topic position

Section 3 of 7

Practice

12 questions

Recall

22 flashcards

Quadratic Sequence Structure

2 1st term 5 2nd term 10 3rd term 17 4th term 26 5th term +3 +5 +7 +9 1st differences +2 +2 +2 2nd differences CONSTANT! nth term formula an² + bn + c a = ½ × (2nd difference)

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Read this section alongside the surrounding pages in Quadratic Sequences. That gives you the full topic sequence instead of a single isolated revision point.

Key FactsFinding the nth Term Formula: The 5-Step MethodThe Basketball ShotWorked Example 1: Basketball Heights

Practice Questions for Quadratic Sequences

Which of the following is a property of a quadratic sequence?

  • A. The first differences are constant
  • B. The second differences are constant
  • C. The terms increase by equal amounts each time
  • D. Every term is a perfect square
1 markfoundation

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.

2 marksstandard

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)

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Finding the nth Term Formula: The 5-Step Method