-1, k and -1 are three consecutive terms of a G.P., then

(i) k = 1

(ii) k = -1

Which of the following is valid ?

1. only 1

2. only 2

3. both 1 and 2

4. either 1 or -1

Given,

-1, k and -1 are three consecutive terms of a G.P.

$\therefore \dfrac{k}{-1} = \dfrac{-1}{k} \\[1em] \Rightarrow k \times k = -1 \times -1 \\[1em] \Rightarrow k^2 = 1 \\[1em] \Rightarrow k = \sqrt{1} = \pm 1.$

Hence, Option 4 is the correct option.