2017 AMC 12A Problems/Problem 7
Problem
Define a function on the positive integers recursively by , if is even, and if is odd and greater than . What is ?
Solution
This is a recursive function, which means the function is used to evaluate itself. To solve this, we must identify the base case, . We also know that when is odd, . Thus we know that . Thus we know that n will always be odd in the recursion of , and we add two each recursive cycle, which there are of. Thus the answer is .
See Also
2017 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 6 |
Followed by Problem 8 |
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All AMC 12 Problems and Solutions |
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