DfE statement A25 · Algebra

The nth term of linear and quadratic sequences

part HigherNon-calculator

The nth term of linear and quadratic sequences is content statement A25 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: "Deduce expressions to calculate the nth term of linear and quadratic sequences." (statement A25). 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 A25

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: "and quadratic". 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

Giving the nth term of 5, 8, 11, 14 as 3n, forgetting the constant. It is 3n + 2 — check by substituting n = 1.
Getting the sign of the constant wrong on a decreasing sequence: 10, 7, 4 has nth term −3n + 13, not −3n + 10.
For a quadratic sequence, using the second difference itself as the coefficient of n² instead of half of it.

Sample questions (10 of 30)

A25 · The nth term of linear and quadratic sequencesQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Algebra

A25

Intermediate

A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

💡 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 the nth term of linear and quadratic sequences on Foundation or Higher?

Both, but not all of it. The parts the DfE prints in bold — "and quadratic" — are Higher only; the rest is Foundation content.

Can I use a calculator for the nth term of linear and quadratic 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?

Giving the nth term of 5, 8, 11, 14 as 3n, forgetting the constant. It is 3n + 2 — check by substituting n = 1.

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.