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  "body": "\n## Summary\n\nIn 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.\n",
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