---
tag: JR6R5F252S
kind: concept
name: Generalized arithmetic progression
aliases: [generalised-arithmetic-progression, multi-dimensional-arithmetic-progression, multidimensional-arithmetic-progression, multiple-arithmetic-progression]
sources:
  - wikipedia: en:2240347@r1373926326
    locator: Generalized arithmetic progression
    note: adopted
    mention: wikipedia://en/2240347
    sections: [Summary]
same_as:
  wikidata: Q5532461
  wikipedia: Generalized arithmetic progression
inventory: [WG5TYC07KW]
---

## Summary

In mathematics, a **generalized arithmetic progression** (or **multiple arithmetic progression**) is a generalization of an arithmetic progression equipped with multiple common differences – whereas an arithmetic progression is generated by a single common difference, a generalized arithmetic progression can be generated by multiple common differences. For example, the [[sequence|0G9EKM0E15]] $17, 20, 22, 23, 25, 26, 27, 28, 29, \dots$ is not an arithmetic progression, but is instead generated by starting with 17 and adding either 3 *or* 5, thus allowing multiple common differences to generate it. A **semilinear set** generalizes this idea to multiple dimensions – it is a set of vectors of integers, rather than a set of integers.