Geometric Progressions
Sequences in which each term is a fixed multiple of the previous one. The model of compound growth, exponential change, and the doubling and halving that pervade computer science.
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Learning Objectives
- Define a geometric progression and recognise its common ratio.
- Derive and apply the formula for the \(n\)-th term.
- Derive and apply the formula for the sum of the first \(n\) terms.
- Model real-world situations of multiplicative change using geometric progressions.
About This Course Unit
Geometric progressions are the multiplicative counterpart of arithmetic progressions: each term arises from the previous one by multiplication by a fixed common ratio rather than by adding a fixed common difference. This single change in operation produces qualitatively different behaviour — exponential growth and decay rather than linear — and explains a great many real-world phenomena, from compound interest to population growth to the time complexity of divide-and-conquer algorithms.