Difference between revisions of "2025 AMC 8 Problems/Problem 4"
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== Solution 1 == | == Solution 1 == | ||
| − | + | We plug <math>a=100, d=-7</math> and <math>n=10</math> into the formula <math>a+d(n-1)</math> for the <math>n</math>th term of an arithmetic sequence whose first term is <math>a</math> and common difference is <math>d</math> to get <math>100-7(10-1) = \boxed{\text{(B)\ 37}}</math>. | |
~Soupboy0 | ~Soupboy0 | ||
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== Solution 2 == | == Solution 2 == | ||
| − | Since we want to find the <math>9</math>th number Lucius says after he says <math>100</math>, our answer is <math>100-(9 \cdot 7) = \boxed{\text{(B)\ 37}}</math> | + | Since we want to find the <math>9</math>th number Lucius says after he says <math>100</math>, <math>7</math> is subtracted from his number <math>9</math> times, so our answer is <math>100-(9 \cdot 7) = \boxed{\text{(B)\ 37}}</math> |
~Sigmacuber | ~Sigmacuber | ||
| − | ==Solution 3 | + | == Solution 3 == |
Using [[brute force]] and counting backward by <math>7</math>s, we have <math>100, 93, 86, 79, 72, 65, 58, 51, 44, \boxed{\text{(B)\ 37}}</math>. | Using [[brute force]] and counting backward by <math>7</math>s, we have <math>100, 93, 86, 79, 72, 65, 58, 51, 44, \boxed{\text{(B)\ 37}}</math>. | ||
| − | Note that this is not | + | Note that this solution is not practical and very time-consuming. |
| − | ~athreyay | + | ~codegirl2013, athreyay |
| − | == | + | == Solution 4 == |
| − | + | This can be thought of as an arithmetic sequence. Knowing that our first term is <math>100</math>, we have to add <math>7</math> to get to our 0th term, <math>107</math>. Our answer is then <math>107 - 10 \cdot 7 = \boxed{\text{(B)\ 37}}</math>. | |
| + | ~Kapurnicus, NYCnerd | ||
| − | == Video Solution 1 | + | == Video Solution 1 == |
| − | + | [//youtu.be/rf5c9ulMA2I ~ ChillGuyDoesMath] | |
| − | + | == Video Solution 2 == | |
| − | + | [//www.youtube.com/jTTcscvcQmI SpreadTheMathLove] | |
| − | == Video Solution by | + | == Video Solution 3 by Daily Dose of Math == |
| − | + | [//youtu.be/rjd0gigUsd0 ~Thesmartgreekmathdude] | |
| − | == Video Solution | + | == Video Solution 4 == |
| − | + | [//youtu.be/PKMpTS6b988 Thinking Feet] | |
| − | + | == Video Solution 5 == | |
| − | == | + | [//youtu.be/VP7g-s8akMY?si=K8Pxs_TQhlR2ntt9&t=211 ~hsnacademy] |
| − | + | == Video Solution 6 == | |
| − | + | [//youtu.be/nwUanrEZpcQ CoolMathProblems] | |
| − | + | ||
| − | + | == Video Solution 7 == | |
| − | == Video Solution | + | |
| − | + | [//youtu.be/Iv_a3Rz725w?si=E0SI_h1XT8msWgkK Pi Academy] | |
== See Also == | == See Also == | ||
Latest revision as of 22:17, 24 February 2025
Contents
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
Solution 4
This can be thought of as an arithmetic sequence. Knowing that our first term is , we have to add to get to our 0th term, 
. Our answer is then 
.
~Kapurnicus, NYCnerd
Video Solution 1
Video Solution 2
Video Solution 3 by Daily Dose of Math
Video Solution 4
Video Solution 5
Video Solution 6
Video Solution 7
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. 
