Generalized arithmetic progression

<p>
In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a generalized arithmetic progression (or multiple arithmetic progression) is a generalization of an <a href="/facts/Arithmetic_progression/c4ew9Xoq">arithmetic progression</a> 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 <a href="/facts/Sequence/gV2S4uqp">sequence</a> 
  
    
      
        17
        ,
        20
        ,
        22
        ,
        23
        ,
        25
        ,
        26
        ,
        27
        ,
        28
        ,
        29
        ,
        …
      
    
    {\displaystyle 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 <i>or</i> 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.
</p>

Generalized arithmetic progression open-in-new

Generalized arithmetic progression