1. The problem is to find the expression for $v_{n+1} - v_n$. 2. This represents the difference between the term at position $n+1$ and the term at position $n$ in a sequence $\{v_n\}$. 3. To solve this, we need the explicit formula or rule for $v_n$ to compute $v_{n+1}$ and then subtract $v_n$. 4. Since the problem does not provide a specific formula for $v_n$, the general expression for the difference is simply: $$v_{n+1} - v_n$$ 5. If $v_n$ is given by a function $f(n)$, then the difference is: $$f(n+1) - f(n)$$ 6. This difference is often called the first difference of the sequence and is used to analyze the behavior of sequences. Since no explicit formula is given, the answer remains the general difference expression.