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an=a1+(n-1)d am+an=a1+(m-1)d+a1+(n-1)d =2a1+(m+n-2)d 同理, ap+aq=2a1+(p-q-2)d 2a1+(m+n-2)d=2a1+(p-q-2)d (m+n)d-2d=(p-q)-2d m+n=p-q 所以,當m+n=p+q時,一定有am+an=ap+aq
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