1. The problem asks to calculate the arithmetic sequence term $u(n)$ given the term number $n-1$. 2. The general formula for the $n$-th term of an arithmetic sequence is: $$u(n) = u(1) + (n-1)d$$ where $u(1)$ is the first term and $d$ is the common difference. 3. Since the problem states $u(n)$ by $n-1$, it suggests the term depends on $n-1$. 4. If we interpret $u(n) = n-1$, then the sequence is defined as: $$u(n) = n - 1$$ 5. This means the first term $u(1) = 1 - 1 = 0$ and the common difference $d = 1$. 6. Therefore, the arithmetic sequence is $0, 1, 2, 3, \ldots$ and the $n$-th term is: $$u(n) = n - 1$$ 7. This matches the given expression, so the calculation is complete.