数列{an}满足a1＝1,a2＝2,an＋2＝2an＋1－an＋2

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数列{an}满足a1＝1,a2＝2,an＋2＝2an＋1－an＋2
数列{an}满足a1＝1,a2＝2,an＋2＝2an＋1－an＋2

数列{an}满足a1＝1,a2＝2,an＋2＝2an＋1－an＋2
（Ⅰ）由an+2=2an+1-an+2得,
an+2-an+1=an+1-an+2,
由bn=an+1-an得,bn+1=bn+2,
即bn+1-bn=2,
又b1=a2-a1=1,
所以{bn}是首项为1,公差为2的等差数列．
（Ⅱ）由（Ⅰ）得,bn=1+2（n-1）=2n-1,
由bn=an+1-an得,an+1-an=2n-1,
则a2-a1=1,a3-a2=3,a4-a3=5,…,an-an-1=2（n-1）-1,
所以,an-a1=1+3+5+…+2（n-1）-1
=
(n−1)(1+2n−3)
2
=（n-1）2,
又a1=1,
所以{an}的通项公式an=（n-1）2+1=n2-2n+2．

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