MathDB

21

Part of 1990 AMC 8

Problems(1)

List Of Numbers

Source:

6/27/2011
A list of 88 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}}}
(A) 164(B) 14(C) 1(D) 2(E) 4 \text{(A)}\ \frac{1}{64}\qquad\text{(B)}\ \frac{1}{4}\qquad\text{(C)}\ 1\qquad\text{(D)}\ 2\qquad\text{(E)}\ 4