2021 AMC 12A Problems/Problem 8
Problem
A sequence of numbers is defined by and
for
. What are the parities (evenness or oddness) of the triple of numbers
, where
denotes even and
denotes odd?
Solution
Making a small chart, we have
$\begin{tabular}{c|c|c|c|c|c|c|c|c|c}$ (Error compiling LaTeX. Unknown error_msg)D_0$&D_1&D_2&D_3&D_4&D_5&D_6&D_7&D_8&D_9\\\hline 0&0&1&1&1&2&3&4&6&9\\\hline E&E&O&O&O&E&O&E&E&O \end{tabular}$ (Error compiling LaTeX. Unknown error_msg)
This starts repeating every 7 terms, so ,
, and
. Thus, the answer is
~JHawk0224
Video Solution by Hawk Math
https://www.youtube.com/watch?v=P5al76DxyHY
See also
2021 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
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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