AMC 8 2025 Problem 4
AMC8 2025 年第 4 题
数列与规律★☆☆☆☆
Lucius is counting backward by 7 s. His first three numbers are 100 , 93 , and 86 . What is his 10 th number?
Lucius正在以7为间隔进行倒数。他倒数的前三个数是100、93和86。请问倒数的第10个数是多少？
- A.30
- B.37
- C.42
- D.44
- E.47
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
this is too complicated so do this instead. we see that 90 is the second term, and if we do 2 times 7 we get 14, but it is 7 off. this tells us our pattern that we times whatever number we are finding by 7 and subtract 7 to that. so we do 7 times 10 to get 70, minus 7 is 63. and 100 minus 63 is 37, meaning our answer is . i tried to explain hope it makes sense We plug a=100, d=-7 and n=10 into the formula a+d(n-1) for the th term of an arithmetic sequence whose first term is and common difference is to get .
Since we want to find the 9 th number Lucius says after he says 100, 7 is subtracted from his number 9 times, so our answer is
Using brute force and counting backward by 7 s, we have .
This can be thought of as an arithmetic sequence. Knowing that our first term is 100, we have to add 7 to get to our 0th term, 107. Our answer is then ., NYCnerd
Setting this as a function f (x)= 100- 7(x-1) where x is the xth number, we can plug in 10 for x. Quick arithmetic gives us the answer of .
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