Arithmetic and geometric progressions, and the one genuinely surprising result in the syllabus: that an infinite sum can be finite, provided the terms shrink fast enough.
Syllabus points covered
- Recognise arithmetic and geometric progressions and use their nth-term formulas
- Use the formulas for the sum of the first n terms of an arithmetic and a geometric progression
- Use the condition |r| < 1 for convergence and find the sum to infinity
- Solve problems involving progressions in context
Common mistakes
- Mixing up the arithmetic and geometric sum formulas under pressure. Identify which one it is first, and write it down.
- Using the sum-to-infinity formula when |r| ≥ 1, where it has no meaning.
- Confusing the nth term with the sum of n terms — read whether the question wants a single term or a total.
- Off-by-one errors: the 10th term uses n = 10, but the sum from the 5th to the 10th is S₁₀ − S₄.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questionsComing soon
- Mark schemeComing soon
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Additional Mathematics past papers