Question

一个“阶梯形”图案由每一行中交替出现的黑白方格组成。图中显示了第 $1$ 行到第 $4$ 行。所有行都以白色方格开始并以白色方格结束。第 $37$ 行中的黑色方格数是

A "stair-step" figure is made up of alternating black and white squares in each row. Rows $1$ through $4$ are shown. All rows begin and end with a white square. The number of black 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

解答：

第 $n$ 行有 $2n - 1$ 个方格。由于两端都是白色且颜色交替，每一行白格比黑格多一个，所以黑格数是 $n - 1$ 。

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 white and the colors alternate, each row has one more white square than black square, so the number of black 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

解答：

其他年份的第 7 题