Question

已知等差数列{an}满足a3·a7=-12,a4+a6=-4,求数列{an}的通项公式.

Answer 1

由题得,因为是等差数列,所以a4+a6=a3+a7=-4

又a3*a7=-12

故a3=-6,a7=2或a3=2,a7=-6

则4d=8或-8,得d=2或-2

当d=2时：an=a5+(n-5)d=-2+2(n-5)=2n-12

当d=-2时：an=a5+(n-5)d=-2-2(n-5)=-2n+8