Difference between revisions of "2017 AMC 12A Problems/Problem 7"
Redjack-512 (talk | contribs) m (→Solution) |
(→Solution) |
||
| Line 8: | Line 8: | ||
<math>\boxed{\textbf{(B)}}</math>. | <math>\boxed{\textbf{(B)}}</math>. | ||
Note that when you write out a few numbers, you find that <math>f(n)=n+1</math> for any <math>n</math>, so <math>f(2017)=2018</math> | Note that when you write out a few numbers, you find that <math>f(n)=n+1</math> for any <math>n</math>, so <math>f(2017)=2018</math> | ||
| + | |||
| + | ==Video Solution (HOW TO THINK CREATIVELY!!!)== | ||
| + | https://youtu.be/ZxcTc-3FoiU | ||
| + | |||
| + | ~Education, the Study of Everything | ||
==See Also== | ==See Also== | ||
{{AMC12 box|year=2017|ab=A|num-b=6|num-a=8}} | {{AMC12 box|year=2017|ab=A|num-b=6|num-a=8}} | ||
Revision as of 13:59, 10 June 2023
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 refers back to itself to calculate subsequent terms. 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 
each recursive cycle, which there are 
of. Thus the answer is 
, which is answer
.
Note that when you write out a few numbers, you find that 
for any , so 
Video Solution (HOW TO THINK CREATIVELY!!!)
~Education, the Study of Everything
See Also
| 2017 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 6 |
Followed by Problem 8 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
