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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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