Difference between revisions of "2016 AMC 12B Problems/Problem 14"

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==Solution==
 
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The second term in a geometric series is <math>a_2 = a_1 \cdot r</math>, where <math>r</math> is the common ratio for the series.
  
 
==See Also==
 
==See Also==
 
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{{AMC12 box|year=2016|ab=B|num-b=13|num-a=15}}
 
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{{MAA Notice}}

Revision as of 12:12, 21 February 2016

Problem

The sum of an infinite geometric series is a positive number $S$, and the second term in the series is $1$. What is the smallest possible value of $S?$

$\textbf{(A)}\ \frac{1+\sqrt{5}}{2} \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ \sqrt{5} \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ 4$

Solution

The second term in a geometric series is $a_2 = a_1 \cdot r$, where $r$ is the common ratio for the series.

See Also

2016 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
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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