Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 10"

 
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==Problem==
<math>10.</math> <math>\{A_n\}_{n \ge 1}</math> is a sequence of positive integers such that
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<math>\{A_n\}_{n \ge 1}</math> is a sequence of positive integers such that
  
 
<math>a_{n} = 2a_{n-1} + n^2</math>
 
<math>a_{n} = 2a_{n-1} + n^2</math>
  
 
for all integers <math>n > 1</math>. Compute the remainder obtained when <math>a_{2004}</math> is divided by <math>1000</math> if <math>a_1 = 1</math>.
 
for all integers <math>n > 1</math>. Compute the remainder obtained when <math>a_{2004}</math> is divided by <math>1000</math> if <math>a_1 = 1</math>.
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==Solution==
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{{solution}}
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==See also==

Revision as of 08:31, 14 February 2008

Problem

$\{A_n\}_{n \ge 1}$ is a sequence of positive integers such that

$a_{n} = 2a_{n-1} + n^2$

for all integers $n > 1$. Compute the remainder obtained when $a_{2004}$ is divided by $1000$ if $a_1 = 1$.

Solution

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See also