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

A. $\frac{1}{3}$
B. $-\frac{1}{3}$
C. -b
D. b
**Answer: Option C**

## Show Answer

Solution(By Apex Team)

$\begin{aligned}&\text{ A.P.is }\frac{1}{3},\frac{1-3b}{3},\frac{1-6b}{3},\ldots\ldots\\
&\Rightarrow\frac{1}{3},\frac{1}{3}-\frac{3b}{3},\frac{1}{3}-\frac{6b}{3},\ldots\ldots\\
&\Rightarrow\frac{1}{3},\frac{1}{3}-b,\frac{1}{3}-2b,\ldots\ldots\\
&\therefore d=\left(\frac{1}{3}-b\right)-\frac{1}{3}\\
&\quad=\frac{1}{3}-b-\frac{1}{3}\\
&=-b\end{aligned}$

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