1990 AMC 8 第 21 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
21.
一个含 个数的数列以前两个给定的数开始。之后每一个新数都是前两个数的乘积。如果最后三个数是 、、，求第一个数。
A list of numbers is formed by beginning with two given numbers. Each new number in the list is the product of the two previous numbers. Find the first number if the last three are :
小提示：
如果某一项是前两项的乘积，那么用这一项除以前一项，就能得到前前一项
If a term is the product of the two before it, then dividing a term by the one just before it recovers the term two positions back
大提示：
从末尾往前倒推，每次用除法填出更早的一项
Work backwards from the end, filling one earlier term at a time by dividing
解答：
因为每一项都是前两项的乘积，所以用某一项除以紧前一项，可以得到它前面第二项。从最后三个数 、、 倒推：
因此完整数列为 、、、、、、、，第一个数是 。
所以正确答案是 B。
Since each term is the product of the two before it, dividing any term by the term just before it recovers the term two positions earlier. Working backwards from the last three terms :
These fill in the earlier terms, giving the full list . The first number is .
Thus, the correct answer is B .
其他年份的第 21 题
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