2017 AMC 10A Problems/Problem 1: Difference between revisions
Solution to problem 1 |
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==Solution== | ==Solution== | ||
Notice this is <math>a_6</math> arithmetic sequence < | Notice this is the term <math>a_6</math> in an arithmetic sequence, such that: | ||
<cmath>\begin{split} | |||
a_1 = 3.\\ | |||
a_n = 2a_(n-1) + 1.\\ | |||
It follows that:\\ | |||
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}</cmath> | |||
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:
![\[\begin{split} a_1 = 3.\\ a_n = 2a_(n-1) + 1.\\ It follows that:\\ a_2 = 3*2 + 1 = 7.\\ a_3 = 7 *2 + 1 = 15.\\ a_4 = 15*2 + 1 = 31.\\ a_5 = 31*2 + 1 = 63.\\ a_6 = 63*2 + 1 = \boxed{\textbf{(C)}\ 127.} \end{split}\]](http://latex.artofproblemsolving.com/d/4/4/d44c8e0ec934c2358018ba4b8426c6455baef6b4.png)
