HMMT 二月 2002 · 冲刺赛 · 第 58 题
HMMT February 2002 — Guts Round — Problem 58
题目详情
- [8] A sequence is defined by a = 1 and a = 2 for n ≥ 1. What is the last digit (in 0 n base 10) of a ? 15
解析
- A sequence is defined by a = 1 and a = 2 for n ≥ 1. What is the last digit (in 0 n base 10) of a ? 15 2 Solution: 6 . Certainly a ≥ 2, so a is divisible by 2 = 4. Writing a = 4 k , we have 13 14 14 4 k k a = 2 = 16 . But every power of 16 ends in 6, so this is the answer. 15