数列{an}是等差数列,a1=f(x+1),a2=0,其中a3=f(x)=x^2-4x+2,求通项公式an

问题描述:

数列{an}是等差数列,a1=f(x+1),a2=0,其中a3=f(x)=x^2-4x+2,求通项公式an

a1=f(x+1)
= (x+1)^2-4(x+1)+2
=x^2-2x-1
a3=x^2-4x+2
d= (a3-a1)/2
=[(x^2-2x-1)-(x^2-4x+2)]/2
= (2x-3)/2
an = a1+(n-1)d
= x^2-2x-1 + (n-1)(2x-3)/2