2025 AMC 8 Problem 4

Attempt Problem 4 of the 2025 AMC 8 below, then check your answer against the video solution and professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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
Answer: B
Concepts:arithmetic sequence
Small hint:
The 1010th number is 99 steps after the 11st
Big hint:
Subtract nine 7s from the first term
Video solution:
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Written solution:
There will be 10−1=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 100−63=37,100 - 63 = 37, which is choice B.
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