sn是an^2和an的等差中项求an通项公式

Question

sn是an^2和an的等差中项 求an通项公式

Answer 1

sn是an^2和an的等差中项
2sn=an^2+an
2sn-1=an-1^2+an-1
2an=an^2+an-(an-1^2+an-1)
an^2-an-(an-1^2+an-1)=0
an^2-an-1^2-(an+an-1)=0
(an+an-1)(an-an-1)-(an+an-1)=0
(an+an-1)(an-an-1-1)=0
an+an-1=0 或an-an-1-1=0
即an/an-1=-1 或 an-an-1=1
即q=-1 或d=1
2sn=an^2+an
2s1=a1^2+a1
2a1=a1^2+a1
a1^2-a1=0
a1(a1-1)=0
a1=0 或 a1=1
当q=-1,a1=0 时
an=a1q^n-1=0
或
当q=-1,a1=1 时
an=a1q^n-1=(-1)^n-1
当d=1,a1=0 时
an=a1+(n-1)d=n-1
或
当d=1,a1=1 时
an=a1+(n-1)d=n