Is a series with the same number for every term a geometric or arithmetic series?

  • 4
    $\begingroup$ Isn't it both? The common difference is $0$ and the common ratio is $1$! $\endgroup$
    – user441558
    Jun 17, 2017 at 3:29
  • $\begingroup$ Or is it neither? $\endgroup$ Jun 17, 2017 at 3:31
  • 1
    $\begingroup$ Well, @ellieff1493, whether it's "both" or "neither" is really just going to depend on the precise definition of arithmetic or geometric progression that you use. $\endgroup$
    – Chris
    Jun 17, 2017 at 3:34
  • $\begingroup$ @ellieff1493 Why is it neither? I know you can't employ the formula for the sum of terms of geometric series $S(n)=a(1-r^n)/(1-r)$ if $r=1$ but that does not mean a sequence like $1,1,1,1,...$ is not geometric! $\endgroup$
    – user441558
    Jun 17, 2017 at 3:36
  • $\begingroup$ And an explanation I found is that arithmetic are linear but geometric aren't $\endgroup$ Jun 17, 2017 at 3:36

1 Answer 1


It's both, and that doesn't tell you anything you didn't already know about constant sequences.

  • $\begingroup$ Except when the series is exactly $0$, the common ratio does not exist. $\endgroup$
    – Frenzy Li
    Jul 16, 2017 at 1:19
  • $\begingroup$ @FrenzyLi Think of geometric series in terms of multiplication, instead of division. You'll see that $0,0,0,\dots$ is not very diferent than $2,2,2,\dots$. $\endgroup$
    – Olivier
    Jul 16, 2017 at 15:19
  • $\begingroup$ You may consider including your comment in the body of the answer, because it is not a trivial observation. $\endgroup$
    – Frenzy Li
    Jul 17, 2017 at 0:49

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