2018
Problem - 4117
Let $a_{0} = 2$, $a_{1} = 5$, and $a_{2} = 8$, and for $n > 2$ define $a_{n}$ recursively to be the remainder when $4$($a_{n-1}$ $+$ $a_{n-2}$ $+$ $a_{n-3}$) is divided by $11$. Find $a_{2018}$ • $a_{2020}$ • $a_{2022}$.
Answer
112
When given a sequence problem, one good thing to do is to check if the sequence repeats itself or if there is a pattern.
After computing more values of the sequence, it can be observed that the sequence repeats itself every 10 terms starting at 
.
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
We can simplify the expression we need to solve to 
• 
• 
.
Our answer is 
• 
• 
.