Difference between revisions of "2014 AMC 12A Problems/Problem 7"
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| − | <math>\sqrt 3</math>, <math>\sqrt[3]3</math>, and <math>\sqrt[6]3</math> which | + | The terms are <math>\sqrt 3</math>, <math>\sqrt[3]3</math>, and <math>\sqrt[6]3</math>, which are equivalent to <math>3^{\frac{3}{6}}</math>, <math>3^{\frac{2}{6}}</math>, and <math>3^{\frac{1}{6}}</math>. So the next term will be <math>3^{\frac{0}{6}}=1</math>, so the answer is <math>\boxed{\textbf{(A)}}</math>. |
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Revision as of 19:46, 7 February 2014
Problem 7
The first three terms of a geometric progression are 
, ![$\sqrt[3]3$](http://latex.artofproblemsolving.com/9/d/f/9df2b093dad7aff038bf8e76013debc0f33465dc.png)
, and ![$\sqrt[6]3$](http://latex.artofproblemsolving.com/f/7/6/f76bf02aeb1d529aef2a4953c053ddaef97334fb.png)
. What is the fourth term?
![$\textbf{(A) }1\qquad \textbf{(B) }\sqrt[7]3\qquad \textbf{(C) }\sqrt[8]3\qquad \textbf{(D) }\sqrt[9]3\qquad \textbf{(E) }\sqrt[10]3\qquad$](http://latex.artofproblemsolving.com/e/1/8/e186a4e2e8aeaae448bf32163d0887f495e72c5a.png)
Solution
The terms are , , and , which are equivalent to 
, 
, and 
. So the next term will be 
, so the answer is 
.
