nine whether the sequence is arithmetic. If so, then find the common difference, \( 10,8,6,4,2, \ldots \) \( 1,2,4,8,16, \ldots \) \( \frac{9}{4}, 2, \frac{7}{4}, \frac{3}{2}, \frac{5}{4}, \ldots \)

To determine if a sequence is arithmetic, we need to check if the difference between consecutive terms is constant. Let's analyze each sequence: 1. \( 10, 8, 6, 4, 2, \ldots \) - The difference between consecutive terms is \( 8 - 10 = -2 \), \( 6 - 8 = -2 \), \( 4 - 6 = -2 \), \( 2 - 4 = -2 \). - Since the difference is constant (-2), this sequence is arithmetic. - The common difference is -2. 2. \( 1, 2, 4, 8, 16, \ldots \) - The difference between consecutive terms is \( 2 - 1 = 1 \), \( 4 - 2 = 2 \), \( 8 - 4 = 4 \), \( 16 - 8 = 8 \). - Since the difference is not constant, this sequence is not arithmetic. 3. \( \frac{9}{4}, 2, \frac{7}{4}, \frac{3}{2}, \frac{5}{4}, \ldots \) - The difference between consecutive terms is \( 2 - \frac{9}{4} = \frac{1}{4} \), \( \frac{7}{4} - 2 = \frac{1}{4} \), \( \frac{3}{2} - \frac{7}{4} = \frac{1}{4} \), \( \frac{5}{4} - \frac{3}{2} = \frac{1}{4} \). - Since the difference is constant (\( \frac{1}{4} \)), this sequence is arithmetic. - The common difference is \( \frac{1}{4} \). Therefore, the first and third sequences are arithmetic, with common differences of -2 and \( \frac{1}{4} \) respectively.