等差数列{an}中,ap=q,aq=p,(p,q∈N,且p≠q),则ap+q=______.
人气:241 ℃ 时间:2020-04-18 22:12:59
解答
设首项为 a1,公差为 d,
则 ap=a1+(p-1)d=q,
aq=a1+(q-1)d=p,
两式相减得 (p-q)d=q-p,
所以解得 d=-1,代入可得 a1=p+q-1,
所以 ap+q=a1+(p+q-1)d=(p+q-1)+(p+q-1)*(-1)=0.
故答案为:0
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