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This topic covers arithmetic and geometric sequences, finding the nth term of a linear sequence, and recognising special sequences such as square, cube and Fibonacci. It's examined right across GCSE and iGCSE Maths. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
For a linear sequence, the common difference is the number in front of n. Multiply n by that difference, then adjust with a constant so the first term is right. For quadratic sequences, take second differences and halve them to get the coefficient of n squared.
Before you start
It draws heavily on substitution and algebraic notation. This is the foundation for nth term rules and series at A-Level.
What you learn
A sequence is a list of numbers following a rule. A term-to-term rule tells you how to get from one term to the next; the nth term rule (or position-to-term rule) gives any term directly from its position. A linear (arithmetic) sequence goes up or down by the same amount each time — the common difference. The nth term of a linear sequence is (common difference) × n + (a number). The course works through term-to-term rules, the nth term of a linear sequence and using the nth term. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Sequences is part of the Algebra strand of our free GCSE maths courses, studied in Foundation tier. The course is built from 3 concept sections, 2 worked examples and 3 check points before the exam-style set. Related topics students usually take next include Simplifying Expressions, Simultaneous Equations, Substitution and Algebraic Fractions. The Algebra revision engine gives you as many extra questions as you want, tracked on your skill tree.
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