Question

The common difference of the A.P.

\[\frac{1}{3}, \frac{1 - 3b}{3}, \frac{1 - 6b}{3}, . . .\] is 

 

Options

• \[\frac{1}{3}\]

   

• \[- \frac{1}{3}\]

   

• −b

• 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
                                       = \[\frac{1 - 3b}{3} - \frac{1}{3}\]

                                       = \[\frac{- 3b}{3} = - b\]