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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