设一列数a1 .a2 .a3 .….a100 中任意三个相邻数之和都是37,已知a2 = 25,a9 = 2x,a99 = 3 x,a100=
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设一列数a1 .a2 .a3 .….a100 中任意三个相邻数之和都是37,已知a2 = 25,a9 = 2x,a99 = 3 x,a100=
设一列数a1 .a2 .a3 .….a100 中任意三个相邻数之和都是37,已知a2 = 25,a9 = 2x,a99 = 3 x,a100=
设一列数a1 .a2 .a3 .….a100 中任意三个相邻数之和都是37,已知a2 = 25,a9 = 2x,a99 = 3 x,a100=
设A1为A,A3为B,那么从A4往下就一直是A;25;B这样重复,即A9与A99都是B,即3x=2x,x就是0,也即是B为0,那么A即为12,所以A100也是12.
∵任意三个相邻数之和都是35,
∴a1+a2+a3=a2+a3+a4=35,a2+a3+a4=a3+a4+a5=35,a3+a4+a5=a4+a5+a6=35,
∴a1=a4,a2=a5,a3=a6,∴a1=a3n+1,a2=a3n+2,a3=a3n,∵20=3×6+2,a20=15,
∴a20=a2=15;∵99=3×33
∴a99=a3,
∵a3=2x,...
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∵任意三个相邻数之和都是35,
∴a1+a2+a3=a2+a3+a4=35,a2+a3+a4=a3+a4+a5=35,a3+a4+a5=a4+a5+a6=35,
∴a1=a4,a2=a5,a3=a6,∴a1=a3n+1,a2=a3n+2,a3=a3n,∵20=3×6+2,a20=15,
∴a20=a2=15;∵99=3×33
∴a99=a3,
∵a3=2x,a99=3-x,
∴3-x=2x,
∴x=1,
∴a3=2,∵a1+a2+a3=35,
∴a1=35-15-2=18,
∵2011=670×3+1,
∴a2011=a1=18.
故答案为18.
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