Term of an Arithmetic Sequence from Its Complement

Given a sequence $S$ of real numbers $b_1$, $b_2$, $b_3$, ..., the complement of $S$ is the sequence $c_1$, $c_2$, $c_3$, ... where $c_1 = 1$ and for each integer $n\geq 2$, $c_n$ satisfies $$c_n = b_1 c_{n-1} + b_2 c_{n-2} + \dots + b_{n-1} c_1$$That is, $c_n$ is the sum of all terms $b_k c_{n-k}$ where $k$ ranges from $1$ to $n-1$. Suppose that $b_1$, $b_2$, $b_3$, ... is an arithmetic sequence and that its complement satisfies $c_{2025} = 3$, $c_{2026} = 0$, $c_{2027} = -3$, $c_{2028} = 3$. Determine the value of $b_{2025}$.