2015 AMC 8 第 18 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。
18.
等差数列是指从第二项开始，每一项都由前一项加上一个常数得到的数列。例如，、、、、 是一个五项等差数列，第一项是 ，每次加上的常数是 。这个 阵列中，每一行和每一列都是五项等差数列。 的值是多少？
An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant to the previous term. For example, is an arithmetic sequence with five terms, in which the first term is and the constant is added. Each row and each column in this array is an arithmetic sequence with five terms. What is the value of
答案：B
小提示：
在五项等差数列中，中间项是首项和末项的平均数
In a five-term arithmetic sequence, the middle term is the average of the first and last terms.
大提示：
将这个事实用于顶行、底行，然后用于中间列
Apply that fact to the top row, bottom row, and then the middle column.
视频讲解：
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文字解答：
在任意五项等差数列中，中间项是首项和末项的平均数。
顶行的中间项为 ，底行的中间项为 。
再对中间列使用同样事实，得 。
所以正确答案是 B。
In any five-term arithmetic sequence, the middle term is the average of the first and last terms.
The middle entry of the top row is and the middle entry of the bottom row is
Now apply the same fact to the middle column:
Thus, B is the correct answer.
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