Difference between revisions of "2017 AMC 10A Problems/Problem 1"
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a_1 = 3.\\ | a_1 = 3.\\ | ||
a_n = 2a_(n-1) + 1.\\ | a_n = 2a_(n-1) + 1.\\ | ||
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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 14:21, 8 February 2017
Problem
What is the value of 
?
Solution
Notice this is the term 
in an arithmetic sequence, such that:
![\[\begin{split} a_1 = 3.\\ a_n = 2a_(n-1) + 1.\\ a_2 = 3*2 + 1 = 7.\\ a_3 = 7 *2 + 1 = 15.\\ a_4 = 15*2 + 1 = 31.\\ a_5 = 31*2 + 1 = 63.\\ a_6 = 63*2 + 1 = \boxed{\textbf{(C)}\ 127.} \end{split}\]](http://latex.artofproblemsolving.com/0/a/d/0add0c9fbccc54abe7b8837be46b1d4216a2309f.png)
