2014 AMC 12A Problems/Problem 7
Contents
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/1/c/e/1ce555f7402c58e7f2bd569b30fd28c2495d9532.png)
Solution
The terms are , , and , which are equivalent to 
, 
, and 
. So the next term will be 
, so the answer is 
.
Video Solution
See Also
| 2014 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 6 |
Followed by Problem 8 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
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