AMC 8 2015 Problem 18

AMC8 2015 年第 18

数列与规律★★★☆☆
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 added is 3. Each row and each column in this 5×5 array is an arithmetic sequence with five terms. The square in the center is labelled X as shown. What is the value of X?
一个等差数列是这样一种数列:第一项后面的每一项,都可以通过把前面一项加上一个常数得到。例如,2,5,8,11,14 是个 5 项的等差数列,其中第 1 项是 2,所加的常数是 3.下图所示的 5x5 的方阵中,每一行每一列都是 5 项的等差数列。正方形中心的数字标记为 X,问 X 的值是多少?
AMC 8 2015 Problem 18 figure
  1. A.21
  2. B.31
  3. C.36
  4. D.40
  5. E.42

正确答案 · Correct Answer

B

解析 · Solution

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