2002 AMC 12P Problems/Problem 2
Problem
The function is given by the table
If and for , find
Solution 1
We can guess that the series given by the problem is periodic in some way. Starting off, is given. so so so so so Plugging in will give us as found before, and plugging in will give and so on. This means that our original guess of the series being periodic was correct. Summing up our findings in a nice table,
\[\begin{tabular}{|c||c|c|c|c|c|} \hline n & 0 & 1 & 2 & 3 & 4 \\ \hline u_n & 4 & 5 & 2 & 1 & 4 \\ \hline \end{tabular}\] (Error compiling LaTeX. Unknown error_msg)
in which the next is found by simply plugging in the number from the last box into The function is periodic every . , and counting starting from will give us our answer of .
See also
2002 AMC 12P (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 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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