DfE statement A24 · Algebra
Special sequences: square, cube, Fibonacci, quadratic, geometric
Special sequences: square, cube, Fibonacci, quadratic, geometric is content statement A24 of the DfE GCSE mathematics subject content, in the algebra area. It is on both tiers, with a Higher-only part, and it is examined without a calculator. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.
What the specification says
The DfE subject content for GCSE mathematics states, verbatim: "Recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (rⁿ where n is an integer, and r is a rational number > 0 or a surd) and other sequences." (statement A24). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "or a surd", "and other sequences". Everything else in the statement is Foundation content.
Calculator
This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.
Common mistakes
- Treating a geometric progression as arithmetic — adding the common ratio rather than multiplying by it.
- Starting a Fibonacci-type sequence from the wrong two terms, so every later term is wrong.
- Confusing triangular numbers (1, 3, 6, 10) with square numbers (1, 4, 9, 16).
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is special sequences: square, cube, Fibonacci, quadratic, geometric on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "or a surd", "and other sequences" — are Higher only; the rest is Foundation content.
Can I use a calculator for special sequences: square, cube, Fibonacci, quadratic, geometric?
Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.
What is the single most common mistake here?
Treating a geometric progression as arithmetic — adding the common ratio rather than multiplying by it.
Are these past paper questions?
No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.
Back to Algebra at Foundation or at Higher.