2006 Cyprus MO/Lyceum/Problem 20
Problem
The sequence 
satisfies 
.
Given that 
, then 
equals
A. 
B. 
C. 
D. 
E. 
Solution
Lets write out a couple of terms:
![\[f(3) = f(2) - f(1) = 0\]](http://latex.artofproblemsolving.com/4/e/e/4ee4c41d8bd58aced8aebf283e7ee4e2987df338.png)
![\[f(4) = f(3) - f(2) = -1, f(5) = f(4) - f(3) = -1, f(6) = f(5)-f(4) = 0\]](http://latex.artofproblemsolving.com/1/8/6/186c4a7f4bac2671eeb8660b672d8bf3098fe089.png)
We quickly see that every third term is zero, so the answer is 
.
See also
| 2006 Cyprus MO, Lyceum (Problems) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
