已知函数f(x)=x^2-4x+2,数列{an}是等差数列,且a1=f(x+1),a2=0,a3=f(x-1),求通项公
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已知函数f(x)=x^2-4x+2,数列{an}是等差数列,且a1=f(x+1),a2=0,a3=f(x-1),求通项公式an与前n项和Sn.
![已知函数f(x)=x^2-4x+2,数列{an}是等差数列,且a1=f(x+1),a2=0,a3=f(x-1),求通项公](/uploads/image/z/8362809-9-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dx%5E2-4x%2B2%2C%E6%95%B0%E5%88%97%7Ban%7D%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E4%B8%94a1%3Df%28x%2B1%29%2Ca2%3D0%2Ca3%3Df%28x-1%29%2C%E6%B1%82%E9%80%9A%E9%A1%B9%E5%85%AC)
a2-a1=a3-a2
-(x+1)^2+4(x+1)-2 = (x-1)^2-4(x-1)+2
2x^2+2-8x+4=0
x^2-4x+3=0
x=1 or 3
if x=1
a1=f(2)=4-8+2=-2
a3=f(0) =2
an = -2+(n-1)2
= 2n-4
Sn = n(a1+an)/2 = n(n-3)
if x=3
a1=f(4)=16-16+2=2
a3=f(2)=4-8+2=-2
an =2-2(n-1)
=4-2n
Sn= (3-n)n
-(x+1)^2+4(x+1)-2 = (x-1)^2-4(x-1)+2
2x^2+2-8x+4=0
x^2-4x+3=0
x=1 or 3
if x=1
a1=f(2)=4-8+2=-2
a3=f(0) =2
an = -2+(n-1)2
= 2n-4
Sn = n(a1+an)/2 = n(n-3)
if x=3
a1=f(4)=16-16+2=2
a3=f(2)=4-8+2=-2
an =2-2(n-1)
=4-2n
Sn= (3-n)n
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