设公差为d,则d≠0.设公比为q.
a2、a3、a6成等比数列,则
a3²=a2·a6
(a1+2d)²=(a1+d)(a1+5d)
整理,得
2a1d+d²=0
d(2a1+d)=0
d=0(舍去)或2a1+d=0
d=-2a1
an=a1+(n-1)d=a1+(-2a1)(n-1)=(3-2n)a1
q=a3/a2=a6/a3=[(3-2×3)a1]/[(3-2×2)a1]=(-3)/(-1)=3
公比q为3.