Question

一位杂货商摆放罐头，最上面一排有一个罐头，每下面一排都比上一排多两个罐头。若这个陈列共有 $100$ 个罐头，它有多少排？

A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains $100$ cans, how many rows does it contain?

$5$

$8$

$9$

$10$

$11$

答案：D

知识点：前n个奇数之和

难度评级：1220

解答：

各排罐头数为 $1, 3, 5, \ldots, (2n - 1)$ ，前 $n$ 个奇数之和为 $n^2$ 。令 $n^2 = 100$ ，得 $n = 10$ 。

因此正确答案是 D。

The rows contain $1, 3, 5, \ldots, (2n - 1)$ cans, and the sum of the first $n$ odd numbers is $n^2.$ Setting $n^2 = 100$ gives $n = 10.$

Thus, the correct answer is D.

2004 AMC 12B 第 8 题

答案：D

难度评级：1220

解答：

其他年份的第 8 题