Sequences - AQA GCSE Mathematics Revision

Topic overview

What you need to know

Sequences is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A sequence where the difference between consecutive terms is constant. E.g. 3, 7, 11, 15 (common difference = 4). The fixed amount added to each term to get the next in an arithmetic sequence. Found by subtracting consecutive terms. The formula for the nth term of an arithmetic sequence: a + (n−1)d, or equivalently dn + (a−d).

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

Arithmetic Sequence: A sequence where the difference between consecutive terms is constant. E.g. 3, 7, 11, 15 (common difference = 4).
Common Difference: The fixed amount added to each term to get the next in an arithmetic sequence. Found by subtracting consecutive terms.
nth Term (Linear): The formula for the nth term of an arithmetic sequence: a + (n−1)d, or equivalently dn + (a−d).
Geometric Sequence: A sequence where each term is found by multiplying the previous term by a constant ratio. E.g. 2, 6, 18, 54.

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

Common Ratio: The fixed multiplier between consecutive terms in a geometric sequence. Found by dividing a term by the previous term.
Quadratic Sequence: A sequence where the second differences are constant. The nth term contains an n² term.
Fibonacci-type Sequence: A sequence where each term is the sum of the two preceding terms. E.g. 1, 1, 2, 3, 5, 8, 13.
Triangular Numbers: Numbers formed by T(n) = n(n+1)/2. The sequence is 1, 3, 6, 10, 15, 21, …

Core knowledge

Key facts for Sequences

8 essentials

Arithmetic Sequence

A sequence where the difference between consecutive terms is constant. E.g. 3, 7, 11, 15 (common difference = 4).

Common Difference

The fixed amount added to each term to get the next in an arithmetic sequence. Found by subtracting consecutive terms.

nth Term (Linear)

The formula for the nth term of an arithmetic sequence: a + (n−1)d, or equivalently dn + (a−d).

Geometric Sequence

A sequence where each term is found by multiplying the previous term by a constant ratio. E.g. 2, 6, 18, 54.

Common Ratio

The fixed multiplier between consecutive terms in a geometric sequence. Found by dividing a term by the previous term.

Quadratic Sequence

A sequence where the second differences are constant. The nth term contains an n² term.

Fibonacci-type Sequence

A sequence where each term is the sum of the two preceding terms. E.g. 1, 1, 2, 3, 5, 8, 13.

Triangular Numbers

Numbers formed by T(n) = n(n+1)/2. The sequence is 1, 3, 6, 10, 15, 21, …

Active recall

Close the notes and answer these

1.Without looking, explain arithmetic sequence and give one example or consequence.
2.Without looking, explain common difference and give one example or consequence.
3.Without looking, explain nth term (linear) and give one example or consequence.
4.Without looking, explain geometric sequence and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

Finished learning?

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