AMC 8 1998 Problem 22

AMC8 1998 年第 22

余数与同余★★★★
Problem 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. A sample sequence: 23,18,9,81,76,.23, 18, 9, 81, 76, \ldots. Find the 98-th term of the sequence that begins 98,49,.98, 49, \ldots.
按照以下三条规则生成一个正整数序列。她从一个正整数开始,然后对结果应用适当的规则,并继续以此方式进行。 规则 1:如果整数小于 10,乘以 9。 规则 2:如果整数为偶数且大于 9,除以 2。 规则 3:如果整数为奇数且大于 9,减去 5。 示例序列:23,18,9,81,76,23, 18, 9, 81, 76, \ldots。 求以 98,49,98, 49, \ldots 开头的序列的第 98 项。
  1. A.6
  2. B.11
  3. C.22
  4. D.27
  5. E.54

正确答案 · Correct Answer

D

解析 · Solution

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