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An arithmetic sequence increases by a fixed common difference d, with nth term a + (n−1)d. This topic covers finding terms, the common difference and the position of a term. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Consecutive terms differ by a constant. The nth term is a plus n minus 1 times d, where a is the first term and d the common difference. The minus one is what catches people out.
Before you start
Bring sequences and substitution with you. The same ideas return in arithmetic series and sigma notation. Pure 2 is where it is assessed.
What you learn
That one formula drives every question here — but at Pure 2 level the conditions are rarely handed to you directly. A quantity changing by a fixed amount each period is arithmetic. The course works through the nth term, both ways, relational conditions → simultaneous equations, three numbers in AP → a quadratic, inequalities, counting, and the first negative term and multi-step application. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Arithmetic Sequences is part of the Sequences & Series strand of our free A-level maths courses, studied in the AS year. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Nearby topics in the same strand are Arithmetic Series, Binomial Expansion (C12) and Binomial Expansion (C34). You can drill this strand further on the Sequences & Series revision engine, with your accuracy saved to your skill tree.
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