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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
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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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