Question

$25$ 个连续偶整数的和是 $10{,}000$ 。这 $25$ 个连续偶整数中最大的是多少？

The sum of $25$ consecutive even integers is $10{,}000.$ What is the largest of these $25$ consecutive even integers?

$360$

$388$

$412$

$416$

$424$

答案：E

知识点：等差数列

难度评级：1100

小提示：

奇数个连续项的平均数就是中间项

For an odd number of consecutive terms, the average is the middle term.

大提示：

有 $12$ 个偶整数比中间项大

There are $12$ even integers larger than the middle term.

视频讲解：

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文字解答：

这些数的平均数为 $\frac{10{,}000}{25} = 400$ 。因为共有二十五个连续偶整数，平均数就是中间项。最大数比中间项大 $12$ 个偶数间隔，所以等于 $400 + 12 \cdot 2 = 424$ 。

所以正确答案是 E。

The average of these numbers is $\frac{10{,}000}{25} = 400.$ The largest number is $12$ even numbers away, which means that it equals $400 + 12 \cdot 2 = 424.$

Thus, E is the correct answer.

2016 AMC 8 第 19 题