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  • Which of the following form an AP? Justify your answer. 1/2,1/3,1/4.......

Which of the following form an AP? Justify your answer. 1/2,1/3,1/4.......

Answers (1)

Answer.          [No]

Solution.        

\begin{aligned} &\text { Here the given series is } \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots \ldots \ldots \text { here } \mathrm{a}_{1}=\frac{1}{2} \mathrm{a}_{2}=\frac{1}{3} \mathrm{a}_{3}=\frac{1}{4}\\ &\mathrm{a}_{2}-\mathrm{a}_{1}=\frac{1}{3}-\frac{1}{2}=\frac{2-3}{6}=\frac{-1}{6}\\ &a_{3}-a_{2}=\frac{1}{4}-\frac{1}{3}=\frac{3-4}{12}=\frac{-1}{12} \end{aligned}

Here the difference of the successive terms is not same. Hence it is not an AP.

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infoexpert21

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