Question

珍娜贝尔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，珍娜贝尔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

小提示：

每日销量是前 $20$ 个正奇数

The daily sales are the first $20$ positive odd numbers.

大提示：

将第一项与最后一项、第二项与倒数第二项依次配对

Pair the first and last terms, second and next-to-last terms, and so on.

视频讲解：

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文字解答：

我们要计算 $1+3 + \cdots + 39\text{。}$ 把两端的项依次配对，可得 $\begin{aligned} &(1+39)+(3+37)+\cdots\\ &\qquad +(19+21) \end{aligned}\text{。}$ 共有 $10$ 对，每对和为 $40$ ，所以 $10\cdot40=400\text{。}$

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