Question:
The common difference of the A.P. $\frac{1}{2 b}, \frac{1-6 b}{2 b}, \frac{1-12 b}{2 b}, \ldots$ is
(a) 2b
(b) −2b
(c) 3
(d) −3
Solution:
Let a be the first term and d be the common difference.
The given A.P. is $\frac{1}{2 b}, \frac{1-6 b}{2 b}, \frac{1-12 b}{2 b}, \ldots$
Common difference = d = Second term − First term
$=\frac{1-6 b}{2 b}-\frac{1}{2 b}$
$=\frac{-6 b}{2 b}=-3$
Hence, the correct option is (d).
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