Question 817320
a, ar, ar^2, ar^3,  are the terms.

{{{a+ar+ar^2+ar^3=5}}}
{{{a(r^3+r^2+r+1)=5}}}
and
{{{a(1+r)=1}}}


You might try multiplying the "1" equation by 5:
5a(r+1)=5*1
5a(r+1)=5
Not useful...


BETTER: You might try dividing the "5" equation's members by the "1" equation's members:
{{{(a(r^3+r^2+r+1))/(a(1+r))=5/1}}}
{{{highlight_green((r^3+r^2+r+1)/(r+1)=5)}}} and this equation should be useful.  From this, try to simplify and use whatever polynomial handling skills you have, like rational roots theorem, remainder, factor theorems...