Choose the correct answer in each of the following questions:

Question:

Choose the correct answer in each of the following questions:

The common difference of the AP $\frac{1}{3}, \frac{1-3 b}{3}, \frac{1-6 b}{3}, \ldots$ is

(a) $\frac{1}{3}$

(b) $\frac{-1}{3}$

(c) $b$

(d) $-b$

Solution:

The given AP is $\frac{1}{3}, \frac{1-3 b}{3}, \frac{1-6 b}{3}, \ldots$

$\therefore$ Common difference, $d=\frac{1-3 b}{3}-\frac{1}{3}=\frac{1-3 b-1}{3}=\frac{-3 b}{3}=-b$

Hence, the correct answer is option D.

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