Write an expression for this arithmetic sequence: \[ 16.5,19,21.5,24,26.5 \ldots \] \( \begin{array}{l}a_{n}=14+2.5(n-1) \\ a_{n}=16.5+2.5(n-1) \\ a_{n}=2.5 n+16.5 \\ a_{n}=19+2.5 n\end{array} \)

To find an expression for the given arithmetic sequence: \[ 16.5, \, 19, \, 21.5, \, 24, \, 26.5, \ldots \] **Step 1: Identify the First Term and Common Difference** - **First term (\(a_1\))**: \(16.5\) - **Common difference (\(d\))**: \(19 - 16.5 = 2.5\) **Step 2: Use the General Formula for an Arithmetic Sequence** The general formula for the \(n\)th term of an arithmetic sequence is: \[ a_n = a_1 + d(n - 1) \] Substituting the known values: \[ a_n = 16.5 + 2.5(n - 1) \] **Step 3: Verify Against the Given Options** Let's check the provided options to see which one matches our derived formula: 1. \(a_n = 14 + 2.5(n - 1)\) - For \(n = 1\): \(14 + 2.5(0) = 14\) (Incorrect, since \(a_1 = 16.5\)) 2. \(a_n = 16.5 + 2.5(n - 1)\) - For \(n = 1\): \(16.5 + 2.5(0) = 16.5\) (Correct) - For \(n = 2\): \(16.5 + 2.5(1) = 19\) (Correct) 3. \(a_n = 2.5n + 16.5\) - For \(n = 1\): \(2.5(1) + 16.5 = 19\) (Incorrect, since \(a_1 = 16.5\)) 4. \(a_n = 19 + 2.5n\) - For \(n = 1\): \(19 + 2.5(1) = 21.5\) (Incorrect, since \(a_1 = 16.5\)) **Conclusion** The correct expression for the arithmetic sequence is: \[ a_n = 16.5 + 2.5(n - 1) \] **Answer:** \[ a_{n}=16.5+2.5(n-1) \]