1998 AMC 8 第 22 题
先试着解答 1998 AMC 8 第 22 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1998 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
22.
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 ：如果整数小于 ，则乘以 。
规则 ：如果整数是偶数且大于 ，则除以 。
规则 ：如果整数是奇数且大于 ，则减去 。
例如，样例序列为 ，，，，，。
求以 、、 开头的这个序列的第 项。
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 If the integer is less than multiply it by
Rule If the integer is even and greater than divide it by
Rule If the integer is odd and greater than subtract from it.
For example, consider the sample sequence
Find the th term of the sequence that begins
小提示：
生成各项，直到某个值重复
Generate terms until a value repeats.
大提示：
循环开始后，把项数按循环长度取余
After the repeat begins, reduce the index modulo the cycle length.
解答：
序列开始为
前三项之后，循环 重复。因为 是 的倍数，第 项是循环中的第五项，即 。
所以正确答案是 D。
The sequence begins
After the first three terms, the cycle repeats. Since is a multiple of the th term is the fifth term of the cycle,
Thus, the correct answer is D .
其他年份的第 22 题
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1999 AMC 8
- 2000 AMC 8
- 2001 AMC 8
- 2002 AMC 8
- 2003 AMC 8
- 2004 AMC 8
- 2005 AMC 8
- 2006 AMC 8
- 2007 AMC 8
- 2008 AMC 8
- 2009 AMC 8
- 2010 AMC 8
- 2011 AMC 8
- 2012 AMC 8
- 2013 AMC 8
- 2014 AMC 8
- 2015 AMC 8
- 2016 AMC 8
- 2017 AMC 8
- 2018 AMC 8
- 2019 AMC 8
- 2020 AMC 8
- 2022 AMC 8
- 2023 AMC 8
- 2024 AMC 8
- 2025 AMC 8
- 2026 AMC 8