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

Solution (By Examveda Team)

$$\eqalign{ & {\text{A}}{\text{.P}}{\text{.is}}\,\,\frac{1}{3},\,\frac{{1 - 3b}}{3},\,\frac{{1 - 6b}}{3},\,...... \cr & \Rightarrow \frac{1}{3},\,\frac{1}{3} - \frac{{3b}}{3},\,\frac{1}{3} - \frac{{6b}}{3},\,...... \cr & \Rightarrow \frac{1}{3},\,\frac{1}{3} - b,\,\frac{1}{3} - 2b,\,....... \cr & \therefore d = \left( {\frac{1}{3} - b} \right) - \frac{1}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{3} - b - \frac{1}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = - b \cr} $$