Difference between revisions of "2017 AMC 10A Problems/Problem 13"
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A pattern starts to emerge as the function is continued. The repeating pattern is <math>0,1,1,2,0,2,2,1\ldots</math> The problem asks for the sum of eight consecutive terms in the sequence. Because there are eight numbers in the repeating sequence, we just need to find the sum of the numbers in the sequence, which is <math>\boxed{\textbf{(D)}\ 9}</math> | A pattern starts to emerge as the function is continued. The repeating pattern is <math>0,1,1,2,0,2,2,1\ldots</math> The problem asks for the sum of eight consecutive terms in the sequence. Because there are eight numbers in the repeating sequence, we just need to find the sum of the numbers in the sequence, which is <math>\boxed{\textbf{(D)}\ 9}</math> | ||
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+ | NOTE: THIS SOLUTION IS CREATED WITH THE ASSUMPTION THAT 2-2=1 (mod 3) AND 1-2=0 (mod 3) | ||
==See Also== | ==See Also== |
Revision as of 18:33, 17 December 2018
Problem
Define a sequence recursively by and the remainder when is divided by for all Thus the sequence starts What is
Solution
A pattern starts to emerge as the function is continued. The repeating pattern is The problem asks for the sum of eight consecutive terms in the sequence. Because there are eight numbers in the repeating sequence, we just need to find the sum of the numbers in the sequence, which is
NOTE: THIS SOLUTION IS CREATED WITH THE ASSUMPTION THAT 2-2=1 (mod 3) AND 1-2=0 (mod 3)
See Also
2017 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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.