等差数列{An},Ap=q,Aq=p,(p不等于q)求Ap+q

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等差数列{An},Ap=q,Aq=p,(p不等于q)求Ap+q等差数列{An},Ap=q,Aq=p,(p不等于q)求Ap+q等差数列{An},Ap=q,Aq=p,(p不等于q)求Ap+qAp=A1+(

等差数列{An},Ap=q,Aq=p,(p不等于q)求Ap+q
等差数列{An},Ap=q,Aq=p,(p不等于q)求Ap+q

等差数列{An},Ap=q,Aq=p,(p不等于q)求Ap+q
Ap=A1+(p-1)d=q
Aq=A1+(q-1)d=p
两式相减
(p-q)d=q-p
d=-1
A1=q-(p-1)(-1)=p+q-1
A(p+q)=A1+(p+q-1)d
=p+q-1+(p+q-1)(-1)
=0
不求A1也可以
A(p+q)=Ap+qd=q+q(-1)=0