Question

数列{an}满足a1=1,a2=2,an+2=2an+1-an+2.(Ⅰ)设bn=an+1-an,

数列{an}满足a1=1,a2=2,an+2=2an+1-an+2.(Ⅰ)设bn=an+1-an,证明{bn}是等差数

Answer 1

a(n+2)=2a(n+1)-an+2
[a(n+2)-a(n+1)]-[a(n+1)-an]=2，为定值
a2-a1=2-1=1
数列{a(n+1)-an}是以1为首项，2为公差的等差数列
bn=a(n+1)-an
数列{bn}是以1为首项，2为公差的等差数列