Question

一位杂货商摆放罐头，最上面一排有一个罐头，每往下一排比上一排多两个罐头。如果这个展示架共有 $100$ 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：1170

解答：

各排罐头数为 $1, 3, 5, \ldots$ ，前 $n$ 个奇数的和为 $n^2$ 。

令 $n^2 = 100$ ，得 $n = 10$ 。

所以正确答案是 D。

The rows hold $1, 3, 5, \ldots$ 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 10B 第 10 题

答案：D

难度评级：1170

解答：

其他年份的第 10 题