Difference between revisions of "2017 AMC 10A Problems/Problem 1"
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==Solution== | ==Solution== | ||
| − | Notice this is the term <math>a_6</math> in | + | Notice this is the term <math>a_6</math> in a recursive sequence, defined recursively as <math>a_1 = 3, a_n = 2a_(n-1) + 1.</math> Thus: |
<cmath>\begin{split} | <cmath>\begin{split} | ||
a_2 = 3*2 + 1 = 7.\\ | a_2 = 3*2 + 1 = 7.\\ | ||
Revision as of 16:29, 8 February 2017
Problem
What is the value of 
?
Solution
Notice this is the term 
in a recursive sequence, defined recursively as 
Thus:
![\[\begin{split} a_2 = 3*2 + 1 = 7.\\ a_3 = 7 *2 + 1 = 15.\\ a_4 = 15*2 + 1 = 31.\\ a_5 = 31*2 + 1 = 63.\\ a_6 = 63*2 + 1 = \boxed{\textbf{(C)}\ 127.} \end{split}\]](http://latex.artofproblemsolving.com/e/1/f/e1fdda04b544cac3e4b07565648aef12b85ea555.png)
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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
