已知数列{An}是等差数列,且Bn=An+A(n+1).求证数列{Bn}是等差数列过程,谢谢

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已知数列{An}是等差数列,且Bn=An+A(n+1).求证数列{Bn}是等差数列过程,谢谢

已知数列{An}是等差数列,且Bn=An+A(n+1).求证数列{Bn}是等差数列过程,谢谢
已知数列{An}是等差数列,且Bn=An+A(n+1).求证数列{Bn}是等差数列
过程,谢谢

已知数列{An}是等差数列,且Bn=An+A(n+1).求证数列{Bn}是等差数列过程,谢谢
B(n+1)-Bn=A(n+1)+A(n+2)-An-A(n+1)
=A(n+2)-An
因为An是等差数列,所以A(n+2)-An=2d 是一个与n无关的常数,所以Bn是等差数列

Bn=a1+(n-1)d+a1+nd=2a1+2nd-d
Bn+1=2a1+2(n+1)d-d
B(n+1)-bn=2d
得证

设An公差为d
B(n+1)=A(n+1)+A(n+2)
B(n+1)-B(n)=A(n+2)-A(n)=2d
所以Bn为等差数列

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