AMC 8 1990 Problem 21

AMC8 1990 年第 21 题

数列与规律★★★☆☆
A list of 8 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 shown:
?‾, ‾, ‾, ‾, ‾,16‾,64‾,1024‾\text{\underline{\hspace{3 mm}?\hspace{3 mm}}\hspace{1 mm},\hspace{1 mm} \underline{\hspace{7 mm}}\hspace{1 mm},\hspace{1 mm} \underline{\hspace{7 mm}}\hspace{1 mm},\hspace{1 mm} \underline{\hspace{7 mm}}\hspace{1 mm},\hspace{1 mm} \underline{\hspace{7 mm}}\hspace{1 mm},\hspace{1 mm}\underline{\hspace{2 mm}16\hspace{2 mm}}\hspace{1 mm},\hspace{1 mm}\underline{\hspace{2 mm}64\hspace{2 mm}}\hspace{1 mm},\hspace{1 mm}\underline{\hspace{1 mm}1024\hspace{1 mm}}}
一个包含 8 个数的列表由两个给定的数开始形成。列表中每个新数都是前两个数的乘积。已知最后三个数如图所示，求第一个数。
  1. A.164\displaystyle \frac{1}{64}
  2. B.14\displaystyle \frac{1}{4}
  3. C.1
  4. D.2
  5. E.4

正确答案 · Correct Answer

B

解析 · Solution

Solution 1

Each missing term must be the quotient of the term two entries after it and the term immediately after it. Therefore, the fifth term is 4, the fourth term is 4, the third is 1, the second is 4, and the first is 14\displaystyle \frac{1}{4}.

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