已知{An}是等差数列,且满足Am=n,An=m,(n不等于m）,求A(m+n).

已知{An}是等差数列,且满足Am=n,An=m,(n不等于m）,求A(m+n).
已知{An}是等差数列,且满足Am=n,An=m,(n不等于m）,求A(m+n).

已知{An}是等差数列,且满足Am=n,An=m,(n不等于m）,求A(m+n).
Am=n
An=m
相减
Am-An=n-m
[A1+(m-1)d]-[A1+(n-1)d]=n-m
(m-n)d=n-m
d=-1
所以A(m+n)
=A1+(m+n-1)d
=A1+(m-1)d+nd
=Am+nd
=n+(-1)n
=0