Which of the following is not an accurate formula to describe the following arithmetic sequence? \( 12,18,24,30, \ldots \) \( 18+6 n \) \( 6+6 n \) \( 12+6(n-1) \) \( 6 n+6 \)

To determine which formula does **not** accurately describe the arithmetic sequence \( 12, 18, 24, 30, \ldots \), let's analyze each option. We'll assume that \( n \) represents the term number in the sequence, starting from \( n = 1 \). ### Given Sequence: - **Term 1 (\( n = 1 \))**: 12 - **Term 2 (\( n = 2 \))**: 18 - **Term 3 (\( n = 3 \))**: 24 - **Term 4 (\( n = 4 \))**: 30 - **...** ### Analyzing Each Formula: 1. **\( 18 + 6n \)** - **For \( n = 1 \)**: \( 18 + 6(1) = 24 \) (Does **not** match term 1: 12) - **Conclusion**: This formula **does not** correctly produce the first term of the sequence when \( n = 1 \). 2. **\( 6 + 6n \)** - **For \( n = 1 \)**: \( 6 + 6(1) = 12 \) (Matches term 1) - **For \( n = 2 \)**: \( 6 + 6(2) = 18 \) (Matches term 2) - **Conclusion**: This formula correctly describes the sequence. 3. **\( 12 + 6(n - 1) \)** - **For \( n = 1 \)**: \( 12 + 6(1 - 1) = 12 \) (Matches term 1) - **For \( n = 2 \)**: \( 12 + 6(2 - 1) = 18 \) (Matches term 2) - **Conclusion**: This formula correctly describes the sequence. 4. **\( 6n + 6 \)** - **For \( n = 1 \)**: \( 6(1) + 6 = 12 \) (Matches term 1) - **For \( n = 2 \)**: \( 6(2) + 6 = 18 \) (Matches term 2) - **Conclusion**: This formula correctly describes the sequence. ### Final Determination: Only **\( 18 + 6n \)** fails to accurately describe the given arithmetic sequence when \( n \) starts at 1. **Answer:** \( 18 + 6 n \) is not an accurate formula for the given arithmetic sequence.