
Ready-to-use resources for teaching geometric sequences to senior maths students. Cover the common ratio, the nth term formula, geometric series and the sum to infinity, with worked examples, differentiated practice and real-world applications like compound interest and population growth.
The resources walk students through the common ratio r, the nth term formula a·r^(n-1), and how to test whether a sequence is geometric. Real-world examples include compound interest, depreciation and population growth, so the algebra connects to something students recognise.
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Lessons move from finding individual terms to summing finite geometric series and evaluating the sum to infinity when |r| < 1. Worked examples show the step-by-step algebra and the common errors to watch for, especially the difference between geometric and arithmetic progressions.
Structured prompts help students articulate why a sequence is geometric, calculate the common ratio from any two consecutive terms, and derive the formula for the nth term. Extension prompts move into sigma notation, geometric series sums and the conditions for convergence to infinity.

Each lesson explains the theory using clear notation and then anchors it in a worked example. Students see how to identify r, substitute into a·r^(n-1), and apply the geometric series formula. Teachers can run the same lesson with stronger or weaker classes by selecting different example sets.
Question sets range from straightforward nth term and common ratio practice through to finite geometric series, sum to infinity and word problems involving compound interest, half-life and recursive savings. Each set includes fully worked solutions so teachers can mark efficiently or hand them straight to students.
Applied tasks ask students to model real situations using a geometric sequence: a savings account compounding annually, a population doubling each generation, or a bouncing ball losing a fixed fraction of its height each bounce. Students set up the sequence, derive r, and solve for a specific term or sum.
- You in approximately four minutes
Comprehensive Teacher Resources for Geometric Sequences
The teacher resources cover the full topic in the order most senior maths courses teach it: defining a geometric sequence, finding the common ratio, deriving the nth term formula a·r^(n-1), summing finite geometric series, and evaluating the sum to infinity when |r| < 1. Worked examples, guided notes and slide decks let teachers run a complete unit without rebuilding materials from scratch.
Targeted Question Sets for Geometric Sequences and Series
The question banks are organised by sub-skill so teachers can target exactly what a class needs. Sections include identifying r and the nth term, solving for a missing term, summing a finite geometric series, applying the sum to infinity formula, and word problems with compound interest, depreciation and recursive growth. Every question has a worked solution.
Engaging Assessments and Applied Activities for Geometric Sequences
Assessment tasks ask students to apply geometric sequences to modelling problems: compound interest schedules, population growth, radioactive half-life, and the total distance travelled by a bouncing ball. Rubrics highlight the algebraic steps students should show, making marking faster and giving clear feedback on where understanding has broken down.