设｛an｝是等差数列

a1=1
a1*a3+a2*a3
=1+2d+(1+d)(1+2d)
=2d^2+5d+1
=2(d+5/4)^2-17/8
所以d=-5/4时，a1*a3+a2*a3最小

｛an｝是等差数列
所以：an=a1+nd = 1+nd
a1*a3+a2*a3=a3*(a1+a2)=(1+3d)*(1+1+2d)=2*[3(d+2/3)^2-1/3]

当d=-2/3时a1*a3+a2*a3最小。

a1*a3+a2*a3=a1*(a1+2d)+(a1+d)*(a1+2d)
=a1^2+2a1d+a1^2+3a1d+2d^2
将a1=1代入上式
得，1+2d+1+3d+2d^2=2d^2+5d+2=2(d^2+5/2d+1)
=2(d+5/4)^2-9/8
要使最小，2(d+5/4)^2满足等于0，所以d=-5/4

a1=1
a1*a3+a2*a3
=1+2d+(1+d)(1+2d)
=2d^2+5d+2
=2(d+5/4)^2-9/8
所以d=-5/4时，a1*a3+a2*a3最小