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 5×55 \times 5 array is an arithmetic sequence with five terms. What is the value of XX? 1   25       X       17   81\begin{array}{|c|c|c|c|c|}\hline 1 & \ & \ & \ & 25 \\ \hline \ & \ & \ & \ & \ \\ \hline \ & \ & X & \ & \ \\ \hline \ & \ & \ & \ & \ \\ \hline 17 & \ & \ & \ & 81 \\ \hline \end{array}
A. 21
B. 31
C. 36
D. 40
E. 42

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Worked solution

1. 2015 AMC 8 官方解析

第一项与第五项差 4 个公差,依次关系填出下表:第一行 1,7,13,19,251, 7, 13, 19, 25;第一列 1,5,9,13,171, 5, 9, 13, 17;第五列 25,39,53,67,8125, 39, 53, 67, 81。中间行首项 9、末项 53,故 X=9+(53−9)÷4×2=31X = 9 + (53 - 9) \div 4 \times 2 = 31。

Answer

B. 31

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