Thread: Six real numbers

A computer programmer claims that he generated six real numbers so that the sum of any four consecutive 's is positive, but the sum of any 3 consecutive 's is negative. Prove that his claim is false.

I think I got it.

a1+a2+a3<0 and a1+a2+a3+a4>0
imply a4>0
Similarly a5>0 and a6>0

a4+a5+a6>0 (Contradiction)