2014 AMC 12A Problems/Problem 7

Problem 7

The first three terms of a geometric progression are $\sqrt 3$ , $\sqrt[3]3$ , and $\sqrt[6]3$ . What is the fourth term?

$\textbf{(A) }1\qquad\textbf{(B) }\sqrt[7]3\qquad\textbf{(C) }\sqrt[8]3\qquad\textbf{(D) }\sqrt[9]3\qquad\textbf{(E) }\sqrt[10]3\qquad$

Solution

The terms are $\sqrt 3$ , $\sqrt[3]3$ , and $\sqrt[6]3$ , which are equivalent to $3^{\frac{3}{6}}$ , $3^{\frac{2}{6}}$ , and $3^{\frac{1}{6}}$ . So the next term will be $3^{\frac{0}{6}}=1$ , so the answer is $\boxed{\textbf{(A)}}$ .

Video Solution

https://youtu.be/rJytKoJzNBY

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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

2014 AMC 12A Problems/Problem 7

Contents

Problem 7

Solution

Video Solution

See Also