Difference between revisions of "2017 AMC 10A Problems/Problem 13"
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==Solution== | ==Solution== | ||
− | 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 | + | 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 pattern, 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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+ | ==Video Solution== | ||
+ | https://youtu.be/s4vnGlwwHHw | ||
+ | |||
+ | https://youtu.be/Y09BGCES_PA | ||
+ | |||
+ | ~savannahsolver | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2017|ab=A|num-b=12|num-a=14}} | {{AMC10 box|year=2017|ab=A|num-b=12|num-a=14}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
+ | |||
+ | [[Category:Introductory Number Theory Problems]] |
Latest revision as of 17:12, 23 July 2021
Contents
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 pattern, we just need to find the sum of the numbers in the sequence, which is
Video Solution
~savannahsolver
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.