8.2. Write down 20 numbers in a row such that the sum of any three consecutive numbers is positive, while the sum of all 20 numbers is negative.
Answer: for example, $-3 ;-3 ; 6.5 ;-3 ;-3 ; 6.5 ;-3 ;-3 ; 6.5 ;-3 ;-3 ; 6.5 ;-3 ;-3 ; 6.5 ;-3 ;-3 ; 6.5 ;-3 ;-3$.

Path to solution: one can assume that the sequence will be periodic

$$
a, a, b, a, a, b, a, a, b, a, a, b, a, a, b, a, a, b, a, a
$$

From this, it follows that $2 a+b>0$ and $14 a+6 b<0$. It is not difficult to find such $a$ and $b$.

Criterion: an example only, without verification - 7 points; the idea of the solution (as described or another) without an example and without an explanation of how to construct the example - 2 points; the idea of the solution with proof that $a$ and $b$ (or some other quantities if the idea is different) exist - 7 points.