1998 AJHSME Problems/Problem 22
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:
Find the term of the sequence that begins
Solution
We could start by looking for a pattern.
From here, we see that we have a pattern of after
Our problem is now really
Find the term of the sequence that goes
There are 5 terms in each repetition of the pattern, and , so the answer is
See also
1998 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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