SOLUTION: In a GP the sum of the 2nd and 3rd terms is 12,and the sum of the 3rd and 4th terms is 60. Find the common ratio and the 1st term.

Algebra ->  Sequences-and-series -> SOLUTION: In a GP the sum of the 2nd and 3rd terms is 12,and the sum of the 3rd and 4th terms is 60. Find the common ratio and the 1st term.       Log On


   

Question 755622: In a GP the sum of the 2nd and 3rd terms is 12,and the sum of the 3rd and 4th terms is 60. Find the common ratio and the 1st term.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Geometric progression: a, ar, ar%5E2, ar%5E3,...

ar%2Bar%5E2=12 and ar%5E2%2Bar%5E3=60

%28ar%5E2%2Bar%5E3%29%2F%28ar%2Bar%5E2%29=5 which is simply dividing second equation by first equation
%28r%5E2%2Br%5E3%29%2F%28r%2Br%5E2%29=5
%28r%2Br%5E2%29%2F%281%2Br%29=5
r%2Br%5E2=5%281%2Br%29
r%5E2%2Br=5r%2B5
r%5E2-4r-5=0
%28r%2B1%29%28r-5%29=0

Either r=-1 or r=5.
The best choice would probably be highlight%28r=5%29.
We still need to find a solution for 'a'.