Difference between revisions of "2017 AMC 10A Problems/Problem 1"
(Created page with "==Problem== What is the value of <math>(2(2(2(2(2(2+1)+1)+1)+1)+1)+1)</math>? <math>\textbf{(A)}\ 70\qquad\textbf{(B)}\ 97\qquad\textbf{(C)}\ 127\qquad\textbf{(D)}\ 159\qqua...") |
(Solution to problem 1) |
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<math>\textbf{(A)}\ 70\qquad\textbf{(B)}\ 97\qquad\textbf{(C)}\ 127\qquad\textbf{(D)}\ 159\qquad\textbf{(E)}\ 729</math> | <math>\textbf{(A)}\ 70\qquad\textbf{(B)}\ 97\qquad\textbf{(C)}\ 127\qquad\textbf{(D)}\ 159\qquad\textbf{(E)}\ 729</math> | ||
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+ | ==Solution== | ||
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+ | Notice this is <math>a_6</math> arithmetic sequence <math>a_1 = 3, a_n = 2a_(n-1) + 1.</math>\\ | ||
+ | <math>a_2 = 3*2 + 1 = 7.</math>\\ | ||
+ | <math>a_3 = 7 *2 + 1 = 15.</math>\\ | ||
+ | <math>a_4 = 15*2 + 1 = 31.</math>\\ | ||
+ | <math>a_5 = 31*2 + 1 = 63.</math>\\ | ||
+ | <math>a_6 = 63*2 + 1 = \boxed{\textbf{(C)}\ 127.}</math> |
Revision as of 15:17, 8 February 2017
Problem
What is the value of ?
Solution
Notice this is arithmetic sequence
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