已知f(x+1)=x^2-2x,等差数列{an}中,a1=f(x-1),a2=-1/2,a3=-f(x),求an及a2+a4+...+a20的值
问题描述:
已知f(x+1)=x^2-2x,等差数列{an}中,a1=f(x-1),a2=-1/2,a3=-f(x),求an及a2+a4+...+a20的值
答
f(x+1)=x²-2x=(x-1)²-1=[(x+1)-2]²-1=(x+1)²-4(x+1)+3f(x)=x²-4x+3a1=f(x-1)=(x-1)²-4(x-1)+3=x²-6x+8a2=-1/2a3=-f(x)=-x²+4x-3a1,a2,a3成等差数列,则2a2=a1+a32(-1/2)=x...