Question

The common difference of the A.P. $\frac{1}{3},\frac{1-3b}{3},\frac{1-6b}{3},...$ is

(a) $\frac{1}{3}$
(b) $-\frac{1}{3}$
(c) −b
(d) b

Answer 1

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

The given A.P. is $\frac{1}{3},\frac{1-3b}{3},\frac{1-6b}{3},...$

Common difference = d = Second term − First term
= $\frac{1-3b}{3}-\frac{1}{3}$
= $\frac{-3b}{3}=-b$

​Hence, the correct option is (c).