A sequence of positive numbers is not necessarily consecutive terms $a, b$, and $c$. We know that

$$
\frac{c-b}{a}+\frac{a-c}{b}+\frac{b-a}{c}=0
$$

Find the difference of the arithmetic sequence.
Solution. Multiply by $a b c$ (where $a, b, c$ are positive):

$$
b c^{2}-b^{2} c+a^{2} c-a c^{2}+a b^{2}-a^{2} b=0
$$

which can also be written as $(a-b)(c-a)(b-c)=0$.

A product is exactly zero if and only if at least one of its factors is 0; therefore, at least two of the three elements are equal. The arithmetic sequence difference is 0, since only in this way can two elements with different indices be equal.