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# Which of the following are APs? If they form an AP, find the common difference $d$ and write three more terms.

$\sqrt3, \sqrt6, \sqrt9, \sqrt{12}, …..$

Given:

Given sequence is $\sqrt3, \sqrt6, \sqrt9, \sqrt{12}, …..$

To do:

We have to check whether the given sequence is an AP. If it is an AP we have to find the common difference $d$ and write three more terms.

Solution:

In the given sequence,

$a_1=\sqrt3, a_2=\sqrt6, a_3=\sqrt9$

$a_2-a_1=\sqrt6-\sqrt3$

$a_3-a_2=\sqrt9-\sqrt6=3-\sqrt6$

$a_2 - a_1 ≠ a_3 - a_2$

Therefore, the given sequence is not an AP.

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