AMC 8 2023 Problem 22
AMC8 2023 年第 22 题
整除与因数★★★☆☆
In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term is 4000. What is the first term?
在一个正整数数列中，第二项之后的每一项都是前面两项的乘积. 数列中的第六项是4000. 问第一项是多少?
- A.1
- B.2
- C.4
- D.5
- E.10
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
In this solution, we will use trial and error to solve. 4000 can be expressed as 200×20. We divide 200 by 20 and get 10, divide 20 by 10 and get 2, and divide 10 by 2 to get 5. No one said that they have to be in ascending order! Solution by ILoveMath31415926535 and clarification edits by apex304 Anonymous question here, if 5 is first term, how do you get 10? (answer to anonymous question) "No one said they had to be in ascending order!" means after 5, the term doesnt need to increase each time.
Consider the first term is and the second term is . Then, the following terms will be , , and . Notice that , then we obtain A=5 and B=2. Solution by Slimeknight, edited by XingZheZhong
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