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.\\ | ||
| − | + | ||
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 14:20, 8 February 2017
Problem
What is the value of 
?
Solution
Notice this is the term 
in an arithmetic sequence, such that:
\[\begin{split}
a_1 = 3.\\
a_n = 2a_(n-1) + 1.\\
a_2 = 3*2 + 1 = 7.\\
a_3 = 7 *2 + 1 = 15.\\
a_4 = 15*2 + 1 = 31.\\
a_5 = 31*2 + 1 = 63.\\
a_6 = 63*2 + 1 = \boxed{\textbf{(C)}\ 127.}
\end{split}\] (Error compiling LaTeX. Unknown error_msg)
