设一列数a1,a2,a3,...,a2010中任意三个相临数之和都是35已知a3=x²+x,a20=15,a99=1+x,那么a2011=_____

Question

设一列数a1,a2,a3,...,a2010中任意三个相临数之和都是35已知a3=x²+x,a20=15,a99=1+x,那么a2011=_____

Answer 1

a1,a2,a3,...,a2010中任意三个相临数之和都是35
a1+a2+a3=35
a2+a3+a4=35
a1=a4,同理,a2=a5,a3=a6
推广a1=a4=a7=...=a(3n+1)
a2=a5=a8=...=a(3n+2)
a3=a6=a9=...=a(3n+3),n=0,1,2,.
a3=a99,x=1或x=-1
a2011=a1=18或20