Difference between revisions of "2017 AMC 10A Problems/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: