2025 AMC 8 Problems/Problem 4

Lucius is counting backward by $7$ s. His first three numbers are $100$ , $93$ , and $86$ . What is his $10$ th number?

$\textbf{(A)}\ 30 \qquad \textbf{(B)}\ 37 \qquad \textbf{(C)}\ 42 \qquad \textbf{(D)}\ 44 \qquad \textbf{(E)}\ 47$

Solution

By the formula for the $n$ th term of an arithmetic sequence, we get that the answer is $a+d(n-1)$ where $a=100, d=-7$ and $n=10$ which is $100 - 7(10 - 1) = \boxed{\text{(B)\ 37}}$ .

~Soupboy0

Solution 2

You could brute force(not really recommended) the sequence, and we get: $100, 93, 86, 79, 72, 65, 58, 51, 44, 37$ Therefore, our answer is $\boxed{\text{(B)\ 37}}$

~athreyay

Vide Solution 1 by SpreadTheMathLove

https://www.youtube.com/watch?v=jTTcscvcQmI

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2025 AMC 8 Problems/Problem 4

Solution

Solution 2

Vide Solution 1 by SpreadTheMathLove