Difference between revisions of "2021 AMC 12A Problems/Problem 8"
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==Problem== | ==Problem== | ||
| − | A sequence of numbers is defined by <math>D_0=0, | + | A sequence of numbers is defined by <math>D_0=0,D_1=0,D_2=1</math> and <math>D_n=D_{n-1}+D_{n-3}</math> for <math>n\ge 3</math>. What are the parities (evenness or oddness) of the triple of numbers <math>(D_{2021},D_{2022},D_{2023})</math>, where <math>E</math> denotes even and <math>O</math> denotes odd? |
<math>\textbf{(A) }(O,E,O) \qquad \textbf{(B) }(E,E,O) \qquad \textbf{(C) }(E,O,E) \qquad \textbf{(D) }(O,O,E) \qquad \textbf{(E) }(O,O,O)</math> | <math>\textbf{(A) }(O,E,O) \qquad \textbf{(B) }(E,E,O) \qquad \textbf{(C) }(E,O,E) \qquad \textbf{(D) }(O,O,E) \qquad \textbf{(E) }(O,O,O)</math> | ||
Revision as of 21:24, 11 February 2021
Contents
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
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
Video Solution (Using parity and pattern finding)
~ pi_is_3.14
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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
