Question

一个“阶梯形”图案由每行中交替出现的涂色和未涂色方格组成。图中显示了第 $1$ 行到第 $4$ 行。所有行都以未涂色方格开始并以未涂色方格结束。第 $37$ 行中的涂色方格数是

A “stair-step” figure is made up of alternating shaded and unshaded squares in each row. Rows $1$ through $4$ are shown. All rows begin and end with an unshaded square. The number of shaded squares in the $37$ th row is

$34$

$35$

$36$

$37$

$38$

答案：C

知识点：找规律基本计数

难度评级：860

小提示：

第 $n$ 行有 $2n - 1$ 个方格，并且从未涂色方格开始、到未涂色方格结束

Row $n$ has $2n - 1$ squares, and they alternate starting and ending with an unshaded square

大提示：

因为两端都是未涂色方格且两种方格交替，所以每行未涂色方格比涂色方格多一个

Since the ends are unshaded and the squares alternate, there is one more unshaded square than shaded square in each row

解答：

第 $n$ 行有 $2n - 1$ 个方格。由于两端都是未涂色方格且两种方格交替，每行未涂色方格比涂色方格多一个，所以涂色方格数是 $n - 1$ 。

对第 $37$ 行，这就是 $37 - 1 = 36$ 。

所以正确答案是 C。

Row $n$ contains $2n - 1$ squares. Because both ends are unshaded and the squares alternate, each row has one more unshaded square than shaded square, so the number of shaded squares is $n - 1.$

For the $37$ th row, this is $37 - 1 = 36.$

Thus, the correct answer is C .

1985 AMC 8 第 7 题

答案：C

难度评级：860

小提示：

大提示：

解答：

其他年份的第 7 题