1. The problem asks to identify which sequence is not a convergent geometric progression. 2. A geometric progression (GP) is a sequence where each term is found by multiplying the previous term by a constant ratio $r$. 3. A GP converges (has a limit) if the absolute value of the ratio $|r| < 1$. 4. Let's analyze each sequence: - A: $2, 3, 4.5, 6.75, \ldots$ Ratio $r = \frac{3}{2} = 1.5$ (greater than 1, so it diverges) - B: $2, \frac{1}{2}, \frac{1}{8}, \frac{1}{32}, \ldots$ Ratio $r = \frac{1/2}{2} = \frac{1}{4} = 0.25$ (less than 1, converges) - C: $-2, 1, -\frac{1}{2}, \frac{1}{4}, \ldots$ Ratio $r = \frac{1}{-2} = -0.5$ (absolute value 0.5 < 1, converges) - D: $-4, -2, -1, -\frac{1}{2}, \ldots$ Ratio $r = \frac{-2}{-4} = 0.5$ (less than 1, converges) - E: $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \ldots$ Ratio $r = \frac{1/4}{1/2} = 0.5$ (less than 1, converges) 5. Only sequence A has $|r| > 1$, so it is not convergent. **Final answer:** Sequence A is not a convergent geometric progression.