2002 AMC 10P Problems/Problem 5
Contents
[hide]Problem
Let be a sequence such that and for all Find
Solution 1
The recursive rule is equal to for all By recursion, If we set and repeat this process times, we will get
Thus, our answer is
Solution 2
Find the first few terms of the sequence and find a pattern.
From here, we can deduce that Plugging in
Thus, our answer is
See also
2002 AMC 10P (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.