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. \( -\frac{1}{4} \)

**Step 1:** Identify the first term \( a_1 \) and the second term \( a_2 \): \[ a_1 = -\frac{1}{2}, \quad a_2 = \frac{3}{4} \] **Step 2:** The common ratio \( r \) in a geometric sequence is given by: \[ r = \frac{a_2}{a_1} \] **Step 3:** Substitute the known values into the formula: \[ r = \frac{\frac{3}{4}}{-\frac{1}{2}} = \frac{3}{4} \times \left(-\frac{2}{1}\right) \] **Step 4:** Perform the multiplication: \[ r = -\frac{6}{4} = -\frac{3}{2} \] **Step 5:** Confirm the result by checking the third term \( a_3 \): \[ a_3 = a_2 \times r = \frac{3}{4} \times \left(-\frac{3}{2}\right) = -\frac{9}{8} \] This matches the given third term. Thus, the common ratio is \[ -\frac{3}{2} \] **Answer:** A. \( -\frac{3}{2} \)