Algebra › Section L · Sequences, series, and the binomial theorem › Topic L.3
Geometric sequences and series
Arithmetic sequences add; geometric sequences multiply. Each term is the previous one times a fixed common ratio - and that one change lets a finite sum telescope into a formula, an infinite sum actually converge, and a repeating decimal become a fraction.
In this topic
- The common ratio
- The general term
- Worked example: a given term
- Worked example: from a list to a formula
- The finite sum, telescoped
- Worked example: a finite sum
- Infinite sums that converge
- Worked example: repeating decimals
- Applications: money multiplies
- Sorting the three sequence types
- Common mistakes to avoid
- Key takeaways
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