Discrete Math › Section E · Sequences › Topic E.2
Arithmetic and geometric sequences
The simplest way for a sequence to change is by the same amount each step, or by the same factor each step. These two patterns, arithmetic and geometric, are the first sequences whose closed formulas we can derive rather than guess, and they mark the line between linear and exponential growth.
In this topic
- Two ways to grow
- Arithmetic sequences
- Why the formula works: telescoping
- Worked example: an arithmetic sequence
- Geometric sequences
- Worked example: a geometric sequence
- Compound growth is geometric
- Linear against exponential growth
- Measuring growth with big-O
- Neither arithmetic nor geometric
- Common mistakes to avoid
- Key takeaways
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