Question

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， $2,5,8,11,14$ 是一个五项等差数列，第一项是 $2$ ，每次加上的常数是 $3$ 。这个 $5\times5$ 阵列中，每一行和每一列都是五项等差数列。 $X$ 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, $2,5,8,11,14$ is an arithmetic sequence with five terms, in which the first term is $2$ and the constant $3$ is added. Each row and each column in this $5\times5$ array is an arithmetic sequence with five terms. What is the value of $X?$

$21$

$31$

$36$

$40$

$42$

答案：B

知识点：等差数列

难度评级：1280

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 $\dfrac{1+25}{2}=13$ ，底行的中间项为 $\dfrac{17+81}{2}=49$ 。

再对中间列使用同样事实，得 $X=\dfrac{13+49}{2}=31$ 。

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 $\dfrac{1+25}{2}=13$ , and the middle entry of the bottom row is $\dfrac{17+81}{2}=49$ .

Now apply the same fact to the middle column: $X=\dfrac{13+49}{2}=31$ .

Thus, B is the correct answer.

2015 AMC 8 第 18 题

答案：B

难度评级：1280

视频讲解：

文字解答：

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