Difference between revisions of "2020 AIME II Problems/Problem 6"
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==Problem== | ==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>. | 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== | ==Video Solution== | ||
Revision as of 20:25, 7 June 2020
Problem
Define a sequence recursively by 
, 
, and![\[t_n = \frac{5t_{n-1}+1}{25t_{n-2}}\]](http://latex.artofproblemsolving.com/0/5/5/055d678205c203b8399cd576b7812bb54597c68a.png)
for all 
. Then 
can be written as 
, where 
and 
are relatively prime positive integers. Find 
.
Video Solution
https://youtu.be/_JTWJxbDC1A ~ CNCM
See Also
| 2020 AIME II (Problems • Answer Key • Resources) | ||
| 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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