1969 AMC 12 第 33 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
33.
设 与 分别为两个等差数列前 项的和。若对所有 都有 ，则第一个数列的第十一项与第二个数列的第十一项之比为：
Let and be the respective sums of the first terms of two arithmetic series. If for all the ratio of the eleventh term of the first series to the eleventh term of the second series is:
无法确定
undetermined
小提示：
在等差数列中，前 项的中间项等于这些项的平均数
In an arithmetic sequence, the middle term of the first terms equals their average
大提示：
将每个第十一项表示为相应的前 项之和除以
Express each eleventh term as its corresponding -term sum divided by
解答：
对等差数列而言，第十一项是前 项的平均数。因此两个数列的第十一项分别为 与 。它们的比为
所以正确答案是 A。
For an arithmetic sequence, the eleventh term is the average of the first terms. Thus the respective eleventh terms are and Their ratio is
Therefore, the correct answer is A.