Difference between revisions of "2020 AIME II Problems/Problem 6"

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==Problem==
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Define a sequence recursively by <math>t_1 = 20</math>, <math>t_2 = 21</math>, and<cmath>t_n = \frac{5t_{n-1}+1}{25t_{n-2}}</cmath>for all <math>n \ge 3</math>. Then <math>t_{2020}</math> can be written as <math>\frac{p}{q}</math>, where <math>p</math> and <math>q</math> are relatively prime positive integers. Find <math>p+q</math>.
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==Video Solution==
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https://youtu.be/_JTWJxbDC1A ~ CNCM
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==See Also==
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{{AIME box|year=2020|n=II|num-b=5|num-a=7}}
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[[Category:Intermediate Algebra Problems]]
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{{MAA Notice}}

Revision as of 21:24, 7 June 2020

Problem

Define a sequence recursively by $t_1 = 20$, $t_2 = 21$, and\[t_n = \frac{5t_{n-1}+1}{25t_{n-2}}\]for all $n \ge 3$. Then $t_{2020}$ can be written as $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.

Video Solution

https://youtu.be/_JTWJxbDC1A ~ CNCM

See Also

2020 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

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