DfE statement A23 · Algebra

Generating sequences

Both tiersNon-calculator

Generating sequences is content statement A23 of the DfE GCSE mathematics subject content, in the algebra area. It is on both tiers, 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: "Generate terms of a sequence from either a term-to-term or a position-to-term rule." (statement A23). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement A23

Tier

Both tiers. This statement is Foundation content, which means Higher students are examined on it too — Higher is Foundation plus more, never instead of it.

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

Using a term-to-term rule to reach the 50th term, which means 49 steps and at least one arithmetic slip.
Substituting the term into a position-to-term rule instead of the position number.
Assuming every sequence is arithmetic and looking only at the first difference.

Sample questions (10 of 30)

A23 · Generating sequencesQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Algebra

A23

Beginner

Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

💡 Hints:

Foundation worksheet Higher worksheet Foundation algebra practice Higher algebra practice

Nearby statements

A1Algebraic notation A2Substitution into formulae A3Expressions, equations, formulae, identities and inequalities A4Simplifying, expanding and factorisingpart Higher

Questions people ask

Is generating sequences on Foundation or Higher?

Both. It is Foundation content, so it can be asked on either tier.

Can I use a calculator for generating sequences?

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?

Using a term-to-term rule to reach the 50th term, which means 49 steps and at least one arithmetic slip.

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.