AMC8 2015

AMC8 2015 · Q18

AMC8 2015 · Q18. It mainly tests Functions basics, Arithmetic sequences basics.

Each row and each column in this 5 × 5 array is an arithmetic sequence with five terms. What is the value of X?

这个5×5阵列中，每行和每列都是一个五项等差数列。X的值是多少？

(A) 21 21

(B) 31 31

(D) 40 40

(E) 42 42

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): The middle number in an arithmetic sequence with $5$ terms is the average of the first and last numbers. The average of $1$ and $25$ is $13$. The average of $17$ and $81$ is $49$. Thus, $X$ is the average of $13$ and $49$, or $31$. Alternatively, $X=\frac{9+53}{2}=31$. In fact $X$ is the average of the four corner entries.

答案（B）：含有 $5$ 项的等差数列中间一项等于首项与末项的平均数。$1$ 与 $25$ 的平均数是 $13$；$17$ 与 $81$ 的平均数是 $49$。因此，$X$ 等于 $13$ 与 $49$ 的平均数，也就是 $31$。或者，$X=\frac{9+53}{2}=31$。实际上，$X$ 等于四个角上数的平均数。

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