设一列数a1、a2,a3,…,a2013中任意三个相邻数之和都相等,已知a3=x,a999=3-2x,那么a2013=_.

问题描述:

设一列数a1、a2,a3,…,a2013中任意三个相邻数之和都相等,已知a3=x,a999=3-2x,那么a2013=______.

∵任意三个相邻数之和都相等,∴a1+a2+a3=a2+a3+a4,a2+a3+a4=a3+a4+a5,a3+a4+a5=a4+a5+a6,∴a1=a4,a2=a5,a3=a6,∴a1=a3n+1,a2=a3n+2,a3=a3n,∵999=3×333,2013=3×671,∴a3=a999=a2013,∴x=3-2x,解得x=...