Question

The common difference of the A.P. $\frac{1}{2b},\frac{1-6b}{2b},\frac{1-12b}{2b},...$ is

(a) 2b
(b) −2b
(c) 3
(d) −3

Answer 1

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

The given A.P. is $\frac{1}{2b},\frac{1-6b}{2b},\frac{1-12b}{2b},...$

Common difference = d = Second term − First term
= $\frac{1-6b}{2b}-\frac{1}{2b}$
= $\frac{-6b}{2b}=-3$

Hence, the correct option is (d).