Question

The general term of the G.P. $$\frac{1}{4}, -\frac{1}{2}, 1, -2, 4, ........$$ is ______.

Options

• $$(-1)^{(n - 1)} \times (2)^{(n - 3)}$$

• $$(-1)^{(n - 1)} \times (2)^{(n - 2)}$$

• $$(-1)^{(n - 1)} \times (-2)^{(n - 1)}$$

• $$(-1)^{(n - 1)} \times (-2)^{(n - 3)}$$

Answer 1

The general term of the G.P. $$\frac{1}{4}, -\frac{1}{2}, 1, -2, 4, ........$$ is `underlinebb((-1)^((n - 1)) xx (2)^((n - 3))`.

Explanation:

Here, $$a = \frac14$$ and $$r = -2$$, so $$T_n = \frac14(-2)^{n - 1} = (-1)^{n - 1}2^{n - 3}$$.