数列是等差数列,a3+a6+a9=3a6=12
a6=4
a3+a9=12-a6=12-4=8
a3·a9=28/a6=28/4=7
a3,a9是方程x^2 -8x+7=0的两根
(x-1)(x-7)=0
x=1或x=7
a3=1,a9=7或a3=7,a9=1
a3=1,a9=7时,a6-a3=3d=4-1=3 d=1
an=a1+(n-1)d=a3+(n-3)d=1+1·(n-3)=n-2
a3=7,a9=1时,a6-a3=3d=4-7=-3 d=-1
an=a1+(n-1)d=a3+(n-3)d=7+(-1)·(n-3)=-n+10
综上,得an=n-2或an=-n+10