Question

Terri 按三条规则生成一个正整数序列。她从一个正整数开始，然后对结果应用合适的规则，并持续这样做。

规则一：如果整数小于十，则乘以九。

规则二：如果整数是偶数且大于九，则除以二。

规则三：如果整数是奇数且大于九，则减去五。

例如，样例序列为 $23, 18, 9, 81, 76, \ldots$ 。

求以下序列的第 $98^\text{th}$ 项： $98, 49, \ldots$

Terri produces a sequence of positive integers by following three rules. She starts with a positive integer, then applies the appropriate rule to the result, and continues in this fashion.

Rule 1: If the integer is less than 10, multiply it by 9.

Rule 2: If the integer is even and greater than 9, divide it by 2.

Rule 3: If the integer is odd and greater than 9, subtract 5 from it.

For example, consider the sample sequence: $23, 18, 9, 81, 76, \ldots .$

Find the $98^\text{th}$ term of the sequence that begins with: $98, 49, \ldots$

$6$

$11$

$22$

$27$

$54$

答案：D

知识点：递推模运算

难度评级：1480

解答：

序列开始为

$\begin{gathered} 98,49,44,22,11, \\ 6,54,27,22,\ldots . \end{gathered}$

前三项之后，循环 $(22,11,6,54,27)$ 重复。因为 $98-3=95$ 是 $5$ 的倍数，第 $98^{\text{th}}$ 项是循环中的第五项，即 $27$ 。

所以正确答案是 D。

The sequence begins

$\begin{gathered} 98,49,44,22,11, \\ 6,54,27,22,\ldots . \end{gathered}$

After the first three terms, the cycle $(22,11,6,54,27)$ repeats. Since $98-3=95$ is a multiple of $5$ , the $98^{\text{th}}$ term is the fifth term of the cycle, $27$ .

Thus, the correct answer is D .

1998 AMC 8 第 22 题

答案：D

难度评级：1480

解答：

其他年份的第 22 题