设一组数列a1,a2,a3...a100中任意三个相邻之和都是37,已知a2=25,a9=2x,a99=3-x,那么a100=?

问题描述:

设一组数列a1,a2,a3...a100中任意三个相邻之和都是37,已知a2=25,a9=2x,a99=3-x,那么a100=?

an+a(n+1)+a(n+2)=a(n+1)+a(n+2)+a(n+3)
所以a(n+3)=an
a9=a99=a3
2x=3-x
x=1
a3=2x=2
a2=25
a100=a1=37-25-2=10