SOLUTION: if the sum of first 4 terms of a gp with the first term 5 is 75 then find its common ratio.

Question 1064925: if the sum of first 4 terms of a gp with the first term 5 is 75 then find its common ratio.
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Not the only way to solve, but,

Rational roots theorem suggests testing for possible roots -2,-1,-7,1,2,7.
Best choice to start would be root of 2.

2    |    1   1   1   -14
     |        2   6   14
     ---------------------
         1    3   7    0

The root that works seems to be 2, since remainder in synthetic division was 0. Binomial factor for the cubic equation includes , so this is the most likely ratio wanted for the question.

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.
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