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A geometric sequence multiplies by a fixed common ratio r, with nth term arⁿ⁻¹. This topic covers finding terms, the common ratio and the conditions for growth, decay or oscillation. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Consecutive terms have a constant ratio. The nth term is a times r to the power n minus 1. Find r by dividing any term by the one before it.
Before you start
You will want index laws and sequences at your fingertips first. It then feeds into geometric series and sum to infinity.
What you learn
Growth and depreciation multiply by a fixed factor each period, so they are geometric. The course works through finding r and a from two terms, show r satisfies a quadratic, three terms in GP: the geometric mean and applications and the smallest n. 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
Geometric Sequences is a Sequences & Series topic in the A-level syllabus, covered here at the AS year. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Related topics students usually take next include Geometric Series, Recurrence Relations, Arithmetic Sequences and Arithmetic Series. The Sequences & Series revision engine gives you as many extra questions as you want, tracked on your skill tree.
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