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

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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(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Not the only way to solve, but,
5%2B5r%2B5r%5E2%2B5r%5E3=75
1%2Br%2Br%5E2%2Br%5E3=15
r%5E3%2Br%5E2%2Br-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. 
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 r-2, so this is the most likely ratio wanted for the question.

highlight%28r=2%29

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.