2025 AMC 8 第 4 题

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4.

Lucius 正在每次减 77 倒着数。他的前三个数是 10010093938686。他的第 1010 个数是多少?

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

答案:B
知识点:等差数列
难度评级:720
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文字解答:

从第一个数到第十个数之间有 101=910 - 1 = 9 个间隔。第一个数是 100100,第 1010 个数前要每次减 77

因此总共减去 9×7=639 \times 7 = 63,从 100100 剩下 10063=37100 - 63 = 37,选 B

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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