2025 AMC 8 第 4 题

先试着解答 2025 AMC 8 第 4 题,然后核对你的答案与视频与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2025 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

4.

Lucius 正在每次减 77 倒着数。他的前三个数是 100100、9393、8686。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
小提示:
第 1010 个数比第 11 个数晚 99 步
The 1010th number is 99 steps after the 11st
大提示:
从第一项连续减去九次七
Subtract nine 7s from the first term
视频讲解:
解答视频缩略图
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文字解答:
从他的第一个数 100100 到第 1010 个数之间有 10−1=910 - 1 = 9 个间隔,每个间隔的大小都是 77。
因此总共减去 9×7=639 \times 7 = 63,从 100100 剩下 100−63=37100 - 63 = 37,选 B。
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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