Write an arithmetic formula, if possible, for the sequence \[ \begin{array}{l}99,97,95,93,91 \ldots \\ a_{n}=-2 n+97 \\ a_{n}=-2 n+99 \\ a_{n}=-2 n \\ a_{n}=-2 n+101\end{array} \]

To find an arithmetic formula for the sequence \( 99, 97, 95, 93, 91, \ldots \), let's analyze the pattern. ### Step 1: Identify the Common Difference An arithmetic sequence has a constant difference between consecutive terms. \[ \begin{align*} 97 - 99 &= -2 \\ 95 - 97 &= -2 \\ 93 - 95 &= -2 \\ 91 - 93 &= -2 \\ \end{align*} \] So, the common difference \( d = -2 \). ### Step 2: Use the Arithmetic Sequence Formula The general formula for the \( n \)-th term of an arithmetic sequence is: \[ a_n = a_1 + (n - 1)d \] Where: - \( a_n \) is the \( n \)-th term, - \( a_1 \) is the first term, - \( d \) is the common difference, - \( n \) is the term number. Given: - \( a_1 = 99 \), - \( d = -2 \), Plugging these into the formula: \[ \begin{align*} a_n &= 99 + (n - 1)(-2) \\ &= 99 - 2n + 2 \\ &= 101 - 2n \\ &= -2n + 101 \end{align*} \] ### Conclusion The correct arithmetic formula for the given sequence is: \[ a_n = -2n + 101 \] **Answer:** The arithmetic formula is \( a_{n} = -2\,n + 101 \).