The common difference of the A.P. is $$\frac{1}{{2q}},$$ $$\frac{{1 - 2q}}{{2q}},$$  $$\frac{{1 - 4q}}{{2q}},$$  . . . . is

Solution (By Examveda Team)

$$\eqalign{ & {\text{A}}{\text{.P}}{\text{.}}\,{\text{is}}\,\frac{1}{{2q}},\,\frac{{1 - 2q}}{{2q}},\,\frac{{1 - 4q}}{{2q}},.... \cr & \Rightarrow \frac{1}{{2q}},\,\left( {\frac{1}{{2q}} - 1} \right),\,\left( {\frac{1}{{2q}} - 2} \right),\,.... \cr & {\text{Clearly}}\,d = \left( {\frac{1}{{2q}} - 1} \right) - \frac{1}{{2q}} \cr & = \frac{1}{{2q}} - 1 - \frac{1}{{2q}} \cr & = - 1 \cr} $$