Question 974847
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.