Lucius is counting backward by 7s. His first three numbers are 100, 93, and 86. What is his 10th number?
A. 30
B. 37
C. 42
D. 44
E. 47

Arithmetic sequences and Gauss summation中文
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Worked solution

1. 2025 AMC 8 官方解析

Answer (B): Lucius's first 10 numbers are

100,93,86,79,72,65,58,51,44,37100, 93, 86, 79, 72, 65, 58, 51, 44, 37

so his 10th number is 37.

OR

To reach the 2nd number, Lucius needs to subtract 7 from 100 once.
To reach the 3rd number, Lucius needs to subtract 7 from 100 twice.
Continuing this pattern, to reach the 10th number, Lucius needs to subtract 7 from 100 a total of 9 times, so his 10th number is 100−9⋅7=100−63=37100 - 9 \cdot 7 = 100 - 63 = 37.

Answer

B. 37

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