Question

Janabel 第一天上班卖出一个小部件。第二天卖出三个。第三天卖出五个，此后每天都比前一天多卖两个。工作 $20$ 天后，Janabel 总共卖出多少个小部件？

On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working $20$ days?

$39$

$40$

$210$

$400$

$401$

答案：D

知识点：等差数列求和

难度评级：960

视频讲解：

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文字解答：

要求这个和可配对为共有 $10$ 对，每对和为 $40$ ，所以 $1+3 + \cdots + 39.$ $\begin{aligned} &(1+39)+(3+37)+\cdots\\ &\qquad +(19+21). \end{aligned}$ $10\cdot40=400.$

所以正确答案是 D。

We want to find $1+3 + \cdots + 39.$ Pairing terms from the ends gives $\begin{aligned} &(1+39)+(3+37)+\cdots\\ &\qquad +(19+21). \end{aligned}$ There are $10$ pairs, and each pair sums to $40.$ Therefore, the sum is $10\cdot40=400.$

Thus, the correct answer is D .

2015 AMC 8 第 9 题

答案：D

难度评级：960

视频讲解：

文字解答：

其他年份的第 9 题