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Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 13"

 
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13. Let <math>a_{n}</math>, <math>b_{n}</math>, and <math>c_{n}</math> be geometric sequences with different common ratios and let <math>a_{n}+b_{n}+c_{n}=d_{n}</math> for all integers <math>n</math>. If <math>d_{1}=1</math>, <math>d_{2}=2</math>, <math>d_{3}=3</math>, <math>d_{4}=-7</math>, <math>d_{5}=13</math>, and <math>d_{6}=-16</math>, find <math>d_{7}</math>.
 
13. Let <math>a_{n}</math>, <math>b_{n}</math>, and <math>c_{n}</math> be geometric sequences with different common ratios and let <math>a_{n}+b_{n}+c_{n}=d_{n}</math> for all integers <math>n</math>. If <math>d_{1}=1</math>, <math>d_{2}=2</math>, <math>d_{3}=3</math>, <math>d_{4}=-7</math>, <math>d_{5}=13</math>, and <math>d_{6}=-16</math>, find <math>d_{7}</math>.
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[[Mock AIME 1 2006-2007]]

Revision as of 15:59, 24 July 2006

13. Let $a_{n}$, $b_{n}$, and $c_{n}$ be geometric sequences with different common ratios and let $a_{n}+b_{n}+c_{n}=d_{n}$ for all integers $n$. If $d_{1}=1$, $d_{2}=2$, $d_{3}=3$, $d_{4}=-7$, $d_{5}=13$, and $d_{6}=-16$, find $d_{7}$.

Mock AIME 1 2006-2007

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