The common difference of the A.P. $\dfrac{1}{k}, \dfrac{1 - k}{k}, \dfrac{1 - 2k}{k}$, …… is :

1. −k

2. k

3. 1

4. −1

Given,

A.P. : $\dfrac{1}{k}, \dfrac{1 - k}{k}, \dfrac{1 - 2k}{k},$ ………

a = $\dfrac{1}{k}$

$\Rightarrow d = \dfrac{1 - k}{k} - \dfrac{1}{k} \\[1em] \Rightarrow d = \dfrac{1 - k - 1}{k} \\[1em] \Rightarrow d = \dfrac{-k}{k} \\[1em] \Rightarrow d = -1.$

Hence, option 4 is the correct option.