2025 AMC 8 Problems/Problem 4
Contents
[hide]Problem
Lucius is counting backward by s. His first three numbers are
,
, and
. What is his
th number?
Solution 1
We plug and
into the formula
for the
th term of an arithmetic sequence whose first term is
and common difference is
to get
.
~Soupboy0
Solution 2
Since we want to find the th number Lucius says after he says
,
is subtracted from his number
times, so our answer is
~Sigmacuber
Solution 3
Using brute force and counting backward by s, we have
.
Note that this solution is not practical and very time-consuming.
~codegirl2013 ~athreyay
Video Solution 1
~ ChillGuyDoesMath
Video Solution by SpreadTheMathLove
https://www.youtube.com/watch?v=jTTcscvcQmI
Video Solution 2 by Daily Dose of Math
~Thesmartgreekmathdude
Video Solution 3 by Thinking Feet
Video Solution 4
https://youtu.be/VP7g-s8akMY?si=K8Pxs_TQhlR2ntt9&t=211 ~hsnacademy
Video Solution 5 by CoolMathProblems
Video Solution 6 by Pi Academy
https://youtu.be/Iv_a3Rz725w?si=E0SI_h1XT8msWgkK
See Also
2025 AMC 8 (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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.