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 an arithmetic sequence, | + | Notice this is the term <math>a_6</math> in an arithmetic sequence, defined recursively as <math>a_1 = 3, a_n = 2a_(n-1) + 1.</math> Thus: |
<cmath>\begin{split} | <cmath>\begin{split} | ||
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| − | |||
a_2 = 3*2 + 1 = 7.\\ | a_2 = 3*2 + 1 = 7.\\ | ||
a_3 = 7 *2 + 1 = 15.\\ | a_3 = 7 *2 + 1 = 15.\\ | ||
Revision as of 15:21, 8 February 2017
Problem
What is the value of 
?
Solution
Notice this is the term 
in an arithmetic 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)
