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