Question

does root 3 ,root 12, root 27, root 48 form an ap
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Answer 1

Answer:

Yes it is forming an AP.

Step-by-step explanation:

√3, 2√3, 3√3, 4√3

So common difference is=2√3-√3=√3(2-1)=√3

Answer 2

We can recall that:

In an A.P. common difference between each consecutive terms will always be equal.

Given:

Sequence:-  $\sqrt{3},\sqrt{12},\sqrt{27},\sqrt{48}$

we have, $a_{1}=\sqrt{3}, a_{2}=\sqrt{12},a_{3}=\sqrt{27},$ and $a_{4}=\sqrt{48}$

$a_{2}-a_1=\sqrt{12}-\sqrt{3}=2\sqrt{3}-\sqrt{3}=\sqrt{3}\\ a_3-a_2=\sqrt{27}-\sqrt{12}=3\sqrt{3}-2\sqrt{3}=\sqrt{3}\\ a_4-a_3=\sqrt{48}-\sqrt{27}=4\sqrt{3}-3\sqrt{3}=\sqrt{3}$

Since, all of the differences are equal to each other

Hence, the above sequence forms an A.P.