SOLUTION: the sum of the second and third terms of a G.P is six times the fourth term. find the two possible values of the common difference.

Question 974847: the sum of the second and third terms of a G.P is six times the fourth term. find the two possible values of the common difference.
Answer by amarjeeth123(569) (Show Source): You can put this solution on YOUR website!
Let the first term of the GP be a.
Let the common ratio be r.
second term=ar
third term=ar^2
fourth term=ar^3
We have ar+ar^2=6ar^3
1+r=6r^2
6r^2-r-1=0
6r^2-3r+2r-1=0
3r(2r-1)+1(2r-1)=0
(3r+1)(2r-1)=0
r=-1/3 or r=1/2
The two possible values of the common difference are r=-1/3 and r=1/2.

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