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

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.

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.

Finding the nth Term Formula: The 5-Step Method