# Difference between revisions of "2017 AMC 12A Problems/Problem 7"

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Define a function on the positive integers recursively by <math>f(1) = 2</math>, <math>f(n) = f(n-1) + 2</math> if <math>n</math> is even, and <math>f(n) = f(n-2) + 2</math> if <math>n</math> is odd and greater than <math>1</math>. What is <math>f(2017)</math>? | Define a function on the positive integers recursively by <math>f(1) = 2</math>, <math>f(n) = f(n-1) + 2</math> if <math>n</math> is even, and <math>f(n) = f(n-2) + 2</math> if <math>n</math> is odd and greater than <math>1</math>. What is <math>f(2017)</math>? | ||

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+ | <math> \textbf{(A)}\ 2017 \qquad\textbf{(B)}\ 2018 \qquad\textbf{(C)}\ 4034 \qquad\textbf{(D)}\ 4035 \qquad\textbf{(E)}\ 4036 </math> |

## Revision as of 15:48, 8 February 2017

## Problem

Define a function on the positive integers recursively by , if is even, and if is odd and greater than . What is ?