6.9 An arithmetic progression has the following property: for any $n$, the sum of its first $n$ terms is equal to $5 n^{2}$. Find the common difference of this progression and its first three terms.
6.9 Using formula (6.3) and the condition of the problem, we get the equality

$$
\frac{2 a_{1}+d(n-1)}{2} n=5 n^{2}, \text{ or } 2 a_{1}-d=(10-d) n
$$

Since in this equality only $n$ can vary, then $d=10$. For $d=10$, we find $a_{1}=5$. Therefore, the first three terms of this progression are: $5 ; 15 ; 25$.

Answer: $5 ; 15 ; 25 ; d=10$.