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Mathematics

The common difference of the A.P. : 13,(1−3p)3,(1−6p)3\dfrac{1}{3}, \dfrac{(1 − 3p)}{3}, \dfrac{(1 − 6p)}{3}, … is:

  1. p

  2. −p

  3. 13\dfrac{1}{3}

  4. −13\dfrac{-1}{3}

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Answer

In the above A.P.,

⇒d=(1−3p)3−13⇒d=(1−3p)−13⇒d=−3p3⇒d=−p.\Rightarrow d = \dfrac{(1 − 3p)}{3} - \dfrac{1}{3} \\[1em] \Rightarrow d = \dfrac{(1 − 3p) - 1}{3} \\[1em] \Rightarrow d = \dfrac{-3p}{3} \\[1em] \Rightarrow d = -p.

Hence, option 2 is the correct option.

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