AMC10每日一题（2000年真题#5）

2000 AMC 10 竞赛试题/第5题

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].