Difference between revisions of "2017 AMC 10A Problems/Problem 1"
(→Solution) |
m (→Solution 2) |
||
Line 18: | Line 18: | ||
==Solution 2== | ==Solution 2== | ||
− | Starting to compute the inner expressions, we see the results are <math>1, 3, 7, 15, \ldots</math>. This is always <math>1</math> less than a power of <math>2</math>. The only admissible answer choice by this rule is thus \boxed{\textbf{(C)}\ 127}. | + | Starting to compute the inner expressions, we see the results are <math>1, 3, 7, 15, \ldots</math>. This is always <math>1</math> less than a power of <math>2</math>. The only admissible answer choice by this rule is thus <math>\boxed{\textbf{(C)}\ 127}</math>. |
==See Also== | ==See Also== | ||
{{AMC10 box|year=2017|ab=A|before=First Problem|num-a=2}} | {{AMC10 box|year=2017|ab=A|before=First Problem|num-a=2}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 18:52, 8 February 2017
Contents
Problem
What is the value of ?
Solution 1
Notice this is the term in a recursive sequence, defined recursively as Thus:
Solution 2
Starting to compute the inner expressions, we see the results are . This is always less than a power of . The only admissible answer choice by this rule is thus .
See Also
2017 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
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 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.