已知数列{an},an属于自然数,sn=1/8(an+2)^2.求｛an}是等差数列
问题描述：
已知数列{an},an属于自然数,sn=1/8(an+2)^2.求｛an}是等差数列
答
sn=1/8(an+2)^2
sn-1=sn=1/8(an-1+2)^2
8an=(an+2)^2-(an-1+2)^2=(an-an-1)(an+an-1+4)
=(an-an-1)(an+an-1)+4an-4an-1
4(an+an-1)=(an-an-1)(an+an-1)
an-an-1=4
｛an}是等差数列