​The eleventh term in the following sequence:​

​$$- \frac{3}{2} + \frac{3}{4} - \frac{3}{8} + \frac{3}{16} - \frac{3}{32} + \cdots$$ is​

Correct option is D

Given:
The sequence is:
​$$- \frac{3}{2} + \frac{3}{4} - \frac{3}{8} + \frac{3}{16} - \frac{3}{32} + \cdots$$

Formula:
​$$T_n = a \cdot r^{n - 1} \\$$

Solution:

$$T_{11} = -\frac{3}{2} \cdot \left(-\frac{1}{2}\right)^{10} \\\ \\= -\frac{3}{2} \cdot \frac{1}{1024} \\\ \\= -\frac{3}{2048} \\\ \\\textbf{Final Answer:} \\{-\frac{3}{2048}}$$

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