Which explicit formula describes the sequence? \( \begin{array}{l}-1,3,7,11, \ldots \\ f(n)=-1+4(n-1) \\ f(n)=(4)(-1)^{n-1} \\ f(n)=(-1)(4)^{n-1} \\ f(n)=4-1(n-1)\end{array} \)

To describe the sequence \(-1, 3, 7, 11, \ldots\), we first recognize that it's an arithmetic sequence where the first term is \(-1\) and the common difference is \(4\). Thus, to find the \(n\)-th term, we can start from the first term and add the product of the common difference and \(n-1\): \[ f(n) = -1 + 4(n - 1) \] This explicit formula correctly captures the \(n\)-th term of the sequence as it starts with \(-1\) and increases by \(4\) for each subsequent term. In a real-world application, understanding sequences like this can help in predicting outcomes in various scenarios, such as budgeting or growth patterns. For example, if a business starts with a deficit of $1, and each month it gains $4, then using the explicit formula to find out how much the business will have after \(n\) months can provide valuable insights for planning future investments or expenditures!