AMC8 2015

AMC8 2015 · Q9

AMC8 2015 · Q9. It mainly tests Arithmetic sequences basics.

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?

Janabel 第一天工作卖了 1 个小部件。第二天卖了 3 个。第三天卖了 5 个，此后每天比前一天多卖 2 个小部件。工作 20 天后，Janabel 总共卖了多少个小部件？

(A) 39 39

(B) 40 40

(D) 400 400

(E) 401 401

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Note that Janabel has sold a total of $1$ widget after $1$ day, $1+3=4=2^2$ after $2$ days and $1+3+5=3^2$ widgets after $3$ days. It can be shown that this pattern continues so that after $20$ days, Janabel has sold a total of $20^2=400$.

答案（D）：注意到 Janabel 在第 1 天后一共卖出 $1$ 个小部件；第 2 天后卖出总数为 $1+3=4=2^2$；第 3 天后卖出总数为 $1+3+5=3^2$ 个。可以证明这个规律会继续下去，因此在第 $20$ 天后，Janabel 一共卖出了 $20^2=400$ 个。

Topics

AR.012 Arithmetic sequences basics