The common difference of the A.P. is 12q,1−2q2q,1−4q2q, ... is

Question:

The common difference of the A.P. is $\frac{1}{2 q}, \frac{1-2 q}{2 q}, \frac{1-4 q}{2 q}, \ldots$ is

(a) −1
(b) 1
(c) q
(d) 2q

Solution:

Let a be the first term and d be the common difference.

The given A.P. is $\frac{1}{2 q}, \frac{1-2 q}{2 q}, \frac{1-4 q}{2 q}, \ldots$

Common difference = d = Second term − First term

$=\frac{1-2 q}{2 q}-\frac{1}{2 q}$

 

$=\frac{-2 q}{2 q}=-1$

Hence, the correct option is (a).

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