Arithmetic Progressions
The first family of sequences with a closed-form general term: those that grow by a fixed amount at each step.
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Learning Objectives
- Define an arithmetic progression and recognise its common difference.
- 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 linear change using arithmetic progressions.
About This Course Unit
An arithmetic progression is a sequence in which each term differs from the previous one by the same amount. This simple condition is enough to determine the entire sequence from its first term and a single number, the common difference. The unit develops the general term, the partial-sum formula, and uses both to model linear change in real situations.