Difference between revisions of "2006 AMC 10B Problems/Problem 18"
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Since <math> 2006 \equiv 2\bmod{6}</math>, | Since <math> 2006 \equiv 2\bmod{6}</math>, | ||
− | <math> a_{2006} = a_2 = | + | <math> a_{2006} = a_2 = \boxed{\textbf{(E) }3}</math> |
== See Also == | == See Also == |
Revision as of 13:51, 7 March 2022
Problem
Let be a sequence for which , , and for each positive integer . What is ?
Solution
Looking at the first few terms of the sequence:
Clearly, the sequence repeats every 6 terms.
Since ,
See Also
2006 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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.