Difference between revisions of "1961 AHSME Problems/Problem 12"
Rockmanex3 (talk | contribs) (Solution to Problem 12) |
Rockmanex3 (talk | contribs) m (→Problem 12) |
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− | == Problem | + | == Problem == |
The first three terms of a geometric progression are <math>\sqrt{2}, \sqrt[3]{2}, \sqrt[6]{2}</math>. Find the fourth term. | The first three terms of a geometric progression are <math>\sqrt{2}, \sqrt[3]{2}, \sqrt[6]{2}</math>. Find the fourth term. | ||
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\textbf{(C)}\ \sqrt[8]{2}\qquad | \textbf{(C)}\ \sqrt[8]{2}\qquad | ||
\textbf{(D)}\ \sqrt[9]{2}\qquad | \textbf{(D)}\ \sqrt[9]{2}\qquad | ||
− | \textbf{(E)}\ \sqrt[10]{2}</math> | + | \textbf{(E)}\ \sqrt[10]{2}</math> |
==Solution== | ==Solution== |
Latest revision as of 16:44, 19 May 2018
Problem
The first three terms of a geometric progression are . Find the fourth term.
Solution
After rewriting the radicals as fractional exponents, the sequence is .
The common ratio of the geometric sequence is . Multiplying that by the third term results in . It simplifies to , so the answer is .
See Also
1961 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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All AHSME Problems and Solutions |
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