A-Level Sequences & Series Revision
Sequences and series revision for A-Level and International A-Level Maths
Sequences and series is one of the most formula-dependent topics on the A-Level course, and one of the easiest to lose marks on through using the right formula for the wrong thing — the sum when the question wanted the nth term, or the arithmetic formula on a geometric sequence. This free revision engine covers the sequences and series content of Edexcel A-Level Maths and the International A-Level Pure 2 and Pure 4 papers, including both the Year 12 and Year 13 treatments of the binomial expansion.
What the sequences and series revision engine covers
Arithmetic sequences — the nth term, finding the common difference, and which term takes a given value Arithmetic series — the sum of n terms, and sigma notation Geometric sequences — the nth term, the common ratio, and finding the smallest n satisfying a condition Geometric series — the sum of n terms, and the sum to infinity when the series converges Binomial expansion for a positive whole power — using binomial coefficients to find a particular term Binomial expansion for a negative or fractional power — the infinite series and its range of validity Recurrence relations — generating terms, and finding the limit of a convergent sequence
Sequences and series formulas you need to know
Arithmetic nth term. uₙ = a + (n − 1)d, where a is the first term and d the common difference. Arithmetic sum. Sₙ = (n/2)(2a + (n − 1)d), or (n/2)(a + l) when you know the last term l. Geometric nth term. uₙ = arⁿ⁻¹, where r is the common ratio. Geometric sum. Sₙ = a(1 − rⁿ)/(1 − r). Sum to infinity. S∞ = a/(1 − r), valid only when |r| < 1. Binomial expansion, positive whole power. The term in xʳ comes from the binomial coefficient nCr multiplied by the appropriate powers. Binomial expansion, any power. (1 + x)ⁿ = 1 + nx + [n(n − 1)/2!]x² + [n(n − 1)(n − 2)/3!]x³ + …, valid for |x|
How to use it
Choose a topic or an exam module. The engine generates a question and marks it instantly, accepting equivalent forms — an exact fraction and its decimal both count where they are genuinely equal. Two hints per question tell you which formula applies and how to set it up, without doing it for you.
More A-Level Maths revision
The binomial expansion for negative and fractional powers feeds directly into approximation questions and into integration by partial fractions, so it is worth being confident with. Track your progress across every topic on the revision hub. All of our revision engines are free.