Question 1064925
Not the only way to solve, but,
{{{5+5r+5r^2+5r^3=75}}}
{{{1+r+r^2+r^3=15}}}
{{{r^3+r^2+r-14=0}}}
    

Rational roots theorem suggests testing for possible roots -2,-1,-7,1,2,7.

Best choice to start would be root of 2.

<pre>
2    |    1   1   1   -14
     |        2   6   14
     ---------------------
         1    3   7    0
</pre>
The root that works seems to be 2, since remainder in synthetic division was 0.  Binomial factor for the cubic equation includes  {{{r-2}}}, so this is the most likely ratio wanted for the question.


{{{highlight(r=2)}}}


check:  5+5*2+5*2*2+5*2*2*2=5+10+20+40=75



You could also use formula for sum of geometric sequence.