2025 AMC 8 Problem 4

Below is the video solution and professionally curated solution for Problem 4 of the 2025 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2025 AMC 8 solutions, or check the answer key.

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Concepts:arithmetic sequence

Difficulty rating: 720

4.

Lucius is counting backward by 77s. His first three numbers are 100,100, 93,93, and 86.86. What is his 1010th number?

3030

3737

4242

4444

4747

Video solution:
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Written solution:

There will be 101=910 - 1 = 9 gaps between his first number 100100 and his 1010th number. Each gap has size 7.7.

So, he will subtract a total of 9×7=639 \times 7 = 63 from 100,100, leaving an answer of 10063=37,100 - 63 = 37, which is choice B.

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