2020 AIME II Problems/Problem 6

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

2020 AIME II (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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2020 AIME II Problems/Problem 6

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