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

Boilanubjaini8f 2022-06-29 Answered
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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Answers (2)

Braedon Rivas
Answered 2022-06-30 Author has 24 answers
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.

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Jackson Duncan
Answered 2022-07-01 Author has 10 answers
0 > ( a + b + c ) + ( b + c + d ) + ( c + d + e ) + ( d + e + f ) = a + 2 b + 3 c + 3 d + 2 e + f .
0 < ( a + b + c + d ) + ( b + c + d + e ) + ( c + d + e + f ) = a + 2 b + 3 c + 3 d + 2 e + f .

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