2025 AMC 8 Problems/Problem 4
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Solution 3 (Not the most practical)
- 5 Video Solution by Pi Academy
- 6 Video Solution 1 (Detailed Explanation) 🚀⚡📊
- 7 Video Solution by SpreadTheMathLove
- 8 Video Solution 2 by Daily Dose of Math
- 9 Video Solution 3 by Thinking Feet
- 10 Video Solution (A Clever Explanation You’ll Get Instantly)
- 11 Video Solution by CoolMathProblems
- 12 See Also
Problem
Lucius is counting backward by 
s. His first three numbers are 
, 
, and 
. What is his 
th number?
Solution 1
By the formula for the 
th term of an arithmetic sequence, we get the answer 
where 
and 
which is equal to 
.
~Soupboy0
Solution 2
Since we want to find the 
th number Lucius says after he says , our answer is 
~Sigmacuber
Solution 3 (Not the most practical)
Using brute force and counting backward by s, we have 
.
Note that this is not the most practical solution, and it is very time-consuming.
~athreyay
Video Solution by Pi Academy
https://youtu.be/Iv_a3Rz725w?si=E0SI_h1XT8msWgkK
Video Solution 1 (Detailed Explanation) 🚀⚡📊
Youtube Link ⬇️
~ 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 (A Clever Explanation You’ll Get Instantly)
https://youtu.be/VP7g-s8akMY?si=K8Pxs_TQhlR2ntt9&t=211 ~hsnacademy
Video Solution by CoolMathProblems
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. 
