2018 AIME II Problems/Problem 2
Contents
[hide]Problem
Let ,
, and
, and for
define
recursively to be the remainder when
(
) is divided by
. Find
•
•
.
Solution 2
Solution
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 •
•
.
See Also
2018 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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