AlgebraDeep Dive

Finding the nth Term Formula: The 5-Step Method

Part of Quadratic Sequences · GCSE GCSE Mathematics revision

This deep dive covers Finding the nth Term Formula: The 5-Step Method 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 4 of 8 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 8

Practice

12 questions

Recall

22 flashcards

Finding the nth Term Formula: The 5-Step Method

To find the formula an² + bn + c for a quadratic sequence, follow these steps:

Step 1: Calculate First Differences

Find the differences between consecutive terms

Step 2: Calculate Second Differences

Find the differences between the first differences

Step 3: Find coefficient 'a'

a = ½ × (second difference)

Step 4: Create sequence an² and find differences

Calculate the differences between original sequence and an²

Step 5: Find 'b' and 'c'

The differences form a linear sequence bn + c

Keep building this topic

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

Quadratic Sequence Structure Worked Example 1: Basketball Heights The Basketball Shot Key Facts

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 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.

12 questions on Quadratic Sequences — practise free

Instant marking, adaptive difficulty, and 22 spaced repetition flashcards. Free until your GCSEs.

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Quadratic Sequence Structure

Worked Example 1: Basketball Heights