1.在以d为公差的等差数列{an}中,设S1=a1+a2+...+an,S2=an+1+an+2+...a2n,S3=a2n+1+a2n+2+...+a3n,求证S1,S2,S3也是等差数列,并求其公差.2.数列{an}是等差数列,a1=f(x+1),a2=0,a3=f(x-1),其中,f(x)=x²-4x+2,求通项公式an.

Question

1.在以d为公差的等差数列{an}中,设
S1=a1+a2+...+an,S2=an+1+an+2+...a2n,S3=a2n+1+a2n+2+...+a3n,求证S1,S2,S3也是等差数列,并求其公差.
2.数列{an}是等差数列,a1=f(x+1),a2=0,a3=f(x-1),其中,f(x)=x²-4x+2,求通项公式an.

Answer 1

1)第1个方法：证明：∵{An}为等差数列 ∴ S1,S2,S3为等差数列 （只需证明S1+S3=2S2即可） 又∵S1+S3=A1+A(2n+1)+A2+A（2n+2)+.An+A(3n) =2A(n+1)+2A(n+2）+.2A(2n) =2S2 ∴S1,S2,S3也为等差数列.第2个方法：S1=n*a1+...