AMC10 2000 A

AMC10 2000 A · Q6

AMC10 2000 A · Q6. It mainly tests Base representation, Sequences in number theory (remainders patterns).

The Fibonacci sequence $1, 1, 2, 3, 5, 8, 13, 21, \dots$ 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?

斐波那契数列 $1, 1, 2, 3, 5, 8, 13, 21, \dots$ 以两个 $1$ 开头，此后每一项是前两项之和。十个数字中，哪个数字是最晚出现在斐波那契数列中某个数的个位上的？

(A) 0 0

(B) 4 4

(D) 7 7

(E) 9 9

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): The sequence of units digits is 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6, ... The digit 6 is the last of the ten digits to appear.

答案（C）：个位数字的序列为 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6, … 数字 6 是十个数字中最后出现的一个。

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