The common ratio of the sequence \( -\frac{1}{2}, \frac{3}{4} \), and \( -\frac{9}{8} \) is A. \( -\frac{3}{2} \) B. \( -\frac{2}{3} \) C. \( -\frac{1}{2} \) D. \( -\frac{1}{4} \)

To find the common ratio of the geometric sequence given, we can divide each term by the preceding term. 1. From the first term \( -\frac{1}{2} \) to the second term \( \frac{3}{4} \): \[ r = \frac{\frac{3}{4}}{-\frac{1}{2}} = \frac{3}{4} \times -2 = -\frac{3}{2} \] 2. From the second term \( \frac{3}{4} \) to the third term \( -\frac{9}{8} \): \[ r = \frac{-\frac{9}{8}}{\frac{3}{4}} = -\frac{9}{8} \times \frac{4}{3} = -\frac{36}{24} = -\frac{3}{2} \] Both calculations yield the same common ratio, confirming that the common ratio of the sequence is \( -\frac{3}{2} \). Thus, the answer is \( \text{A. } -\frac{3}{2} \).