2025 AMC 8

Complete problem set with solutions and individual problem pages

Problem 4 Easy

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

Answer:B

Solution 1

We plug a=100, d=-7 and n=10 into the formula a+d(n-1) for the nth term of an arithmetic sequence whose first term is a and common difference is d to get 100-7(10-1) = \boxed{\text{(B) 37}}.

 

Solution 2

Since we want to find the 9th number Lucius says after he says 100, 7 is subtracted from his number 9 times, so our answer is 100-(9 \cdot 7) = \boxed{\text{(B) 37}}

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