Question 755622
Geometric progression:  {{{a}}}, {{{ar}}}, {{{ar^2}}}, {{{ar^3}}},...


{{{ar+ar^2=12}}} and {{{ar^2+ar^3=60}}}


{{{(ar^2+ar^3)/(ar+ar^2)=5}}} which is simply dividing second equation by first equation
{{{(r^2+r^3)/(r+r^2)=5}}}
{{{(r+r^2)/(1+r)=5}}}
{{{r+r^2=5(1+r)}}}
{{{r^2+r=5r+5}}}
{{{r^2-4r-5=0}}}
{{{(r+1)(r-5)=0}}}


Either {{{r=-1}}} or {{{r=5}}}.

The best choice would probably be {{{highlight(r=5)}}}.
We still need to find a solution for 'a'.