# 6 real numbers, sum of any 3 consecutive is negative, while sum of any 4 consecutive is positive. Pr

6 real numbers, sum of any 3 consecutive is negative, while sum of any 4 consecutive is positive. Prove false.
A computer programmer claims that he generated six real numbers ${a}_{1},{a}_{2}...{a}_{6}$ so that the sum of any four consecutive ${a}_{i}$ is positive, but the sum of any three consecutive ${a}_{i}$ is negative. Prove that his claim is false.
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Braedon Rivas
Consider the simulataneous inequalties
$a+b+c+d>0,$
$a+b+c<0,$
$b+c+d<0.$
What can we say about the sign of $a$? What about the sign of $d$?
If you have a sequence of six numbers, it has three subsequences each consisting of four consecutive numbers. Consider what each of them tells you about numbers in the original sequence.

Jackson Duncan
$0>\left(a+b+c\right)+\left(b+c+d\right)+\left(c+d+e\right)+\left(d+e+f\right)=a+2b+3c+3d+2e+f.$
$0<\left(a+b+c+d\right)+\left(b+c+d+e\right)+\left(c+d+e+f\right)=a+2b+3c+3d+2e+f.$