Mathematics (AS)·Sequences and series · NSSCAS 1.2.3
Geometric progressions
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Some patterns grow by multiplying, not adding — and they grow fast! In this lesson you will learn to recognise a geometric progression by its constant ratio, find any term with the formula uₙ = arⁿ⁻¹, and add up the first n terms with a formula you will derive yourself. We finish with a real Namibian savings problem, so you can see geometric progressions working with actual money. By the end, APs and GPs will both feel like old friends.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.2.3):
- Recognise a geometric progression by testing neighbouring terms for a constant common ratio, including negative ratios.
- Use the formula for the nth term, uₙ = arⁿ⁻¹, to find terms, to find a and r from two given terms, and to find which term first exceeds a given value.
- Use the formula for the sum of the first n terms, Sₙ = a(1−rⁿ)/(1−r) or a(rⁿ−1)/(r−1), to solve problems involving geometric progressions, including real-life compound contexts.
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