5. Which statement is not true about the arithmetic sequence: \( 14,20,26,32, \ldots \) p A. The 5 th term is 38 . B. The 9 th term is 68 . C. The common difference is 6 . D. The 3rd term is 26 . b c

To determine which statement is not true about the arithmetic sequence \( 14, 20, 26, 32, \ldots \), we first identify the common difference and then calculate the terms as needed. 1. **Common Difference**: The common difference \( d \) can be calculated as: \[ d = 20 - 14 = 6 \] So, the common difference is indeed 6. 2. **Finding the 5th term**: The \( n \)-th term of an arithmetic sequence can be calculated using the formula: \[ a_n = a_1 + (n-1) \cdot d \] where \( a_1 \) is the first term and \( d \) is the common difference. For the 5th term (\( n = 5 \)): \[ a_5 = 14 + (5-1) \cdot 6 = 14 + 4 \cdot 6 = 14 + 24 = 38 \] So, statement A is true. 3. **Finding the 9th term**: For the 9th term (\( n = 9 \)): \[ a_9 = 14 + (9-1) \cdot 6 = 14 + 8 \cdot 6 = 14 + 48 = 62 \] So, statement B is not true (it claims the 9th term is 68). 4. **Finding the 3rd term**: For the 3rd term (\( n = 3 \)): \[ a_3 = 14 + (3-1) \cdot 6 = 14 + 2 \cdot 6 = 14 + 12 = 26 \] So, statement D is true. Based on the calculations, the statement that is not true is: **B. The 9th term is 68.**