[ Examples and counterexamples. Constructions $\quad]$ [ Linear inequalities and systems of inequalities $]$

Can 20 numbers be written in a row so that the sum of any three consecutive numbers is positive, while the sum of all 20 numbers is negative?
Consider 20 numbers $a, b, b, a, b, b, \ldots, a, b, b, a, b$. The sum of three consecutive numbers is $a+2 b$. The sum of all numbers is $7 a+13 b$. Therefore, it is sufficient to choose $a$ and $b$ such that $a+2 b>0$ and $7 a+13 b<0$. For example, we can set $a=-25, b=13$.

## Answer

We can.