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

Boilanubjaini8f

Boilanubjaini8f

Answered question

2022-06-29

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.

Answer & Explanation

Braedon Rivas

Braedon Rivas

Beginner2022-06-30Added 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.
Jackson Duncan

Jackson Duncan

Beginner2022-07-01Added 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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