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  • Which of the following form an AP? Justify your answer. root3,root12,root 27, root 48 , ....

Which of the following form an AP? Justify your answer. root3,root12,root 27, root 48 , ....

Answers (1)

Answer.          [Yes]

Solution.        

\begin{aligned} &\text { Here the given series is } \sqrt{3}, \sqrt{12}, \sqrt{27}, \sqrt{48}, \ldots . \text { here } \mathrm{a}_{1}=\sqrt{3} \mathrm{a}_{2}=\sqrt{12} \mathrm{a}_{3}=\sqrt{27}\\ &a_{4}=\sqrt{48}\\ &a_{2}-a_{1}=\sqrt{12}-\sqrt{3}=2 \sqrt{3}-\sqrt{3}=\sqrt{3}=\sqrt{3}(2-1)=\sqrt{3}\\ &a_{3}-a_{2}=\sqrt{27}-\sqrt{12}=3 \sqrt{3}-2 \sqrt{3}=\sqrt{3}\\ &a_{4}-a_{3}=\sqrt{48}-\sqrt{27}=4 \sqrt{3}-3 \sqrt{3}=\sqrt{3} \end{aligned}

Here the difference of the successive term is same. Hence it is an AP.

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