Difference between revisions of "2021 AMC 10A Problems/Problem 4"
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==Video Solution 4== | ==Video Solution 4== |
Revision as of 16:44, 7 March 2021
Contents
Problem
A cart rolls down a hill, travelling inches the first second and accelerating so that during each successive -second time interval, it travels inches more than during the previous -second interval. The cart takes seconds to reach the bottom of the hill. How far, in inches, does it travel?
Solution 1 (Arithmetic Series)
Since we seek the sum in which there are addends. The last addend is Therefore, the requested sum is Recall that to find the sum of an arithmetic series, we take the average of the first and last terms, then multiply by the number of terms, namely ~MRENTHUSIASM
Solution 2 (Answer Choices and Modular Arithmetic)
From the -term sum in the previous solution, taking modulo gives The only answer choices that are are and By a quick estimation, is too small, leaving us with
~MRENTHUSIASM
Video Solution (Arithmetic Sequence but in a different way)
https://www.youtube.com/watch?v=sJa7uB-UoLc&list=PLexHyfQ8DMuKqltG3cHT7Di4jhVl6L4YJ&index=4
~ North America Math Contest Go Go Go
Video Solution (Using Arithmetic Sequence)
~ pi_is_3.14
Video Solution 4
~savannahsolver
Video Solution by TheBeautyofMath
https://youtu.be/50CThrk3RcM?t=262
~IceMatrix
See Also
2021 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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.