AMC12每日一题（2000年真题#03）

2000 AMC 12竞赛试题/第3题

The following problem is from both  the 2000 AMC 12 #4 and 2000 AMC 10 #6, so both problems redirect to this  page.

Problem

The Fibonacci sequence 1,1,2,3,5,8,13,21,... starts  with two 1s, and each term afterwards is the sum of its two predecessors. Which  one of the ten digits is the last to appear in the units position of a number in  the Fibonacci sequence?

(A)  0  (B)  4(C)  6(D)  7(E)   9  

Solution

Note that any digits other than the units digit will  not affect the answer. So to make computation quicker, we can just look at the  Fibonacci sequence in mod10:

1,1,2,3,5,8,3,1,4,5,9,4,3,7,0,7,7,4,1,5,6,....

The last digit to appear in the units position of a number in the  Fibonacci sequence is 6.[C]