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

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

Explanation:

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

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

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