GCSE Maths: Sequences Revision Guide

Arithmetic sequences

In an arithmetic sequence, the difference between consecutive terms is constant. The nth term formula is an + b, where a is the common difference and b is found by working out what adjusts the first term to fit.

Finding the nth term

To find the nth term of an arithmetic sequence, first find the common difference (a), then check what needs to be added or subtracted so the formula gives the correct first term when n = 1.

Quadratic sequences

In a quadratic sequence, the second difference (the difference between the differences) is constant. The nth term includes an n² term, where the coefficient of n² is half the second difference.

Special sequences

Know common sequence types: square numbers (1, 4, 9, 16...), triangular numbers (1, 3, 6, 10...), and the Fibonacci sequence, where each term is the sum of the two before it.

Common mistakes

• Forgetting to check the nth term formula against more than one term in the sequence.
• Using the first difference instead of the second difference for quadratic sequences.
• Mixing up triangular and square number patterns.