Question

Question 1 (vii)
Which of the following form an AP? Justify your answer.
$\sqrt{3},\sqrt{12},\sqrt{27},\sqrt{48}\cdots$

Answer 1

$\sqrt{3},\sqrt{12},\sqrt{27},\sqrt{48},\cdots i.e.\sqrt{3},2\sqrt{3},3\sqrt{3},4\sqrt{3},\cdots \cdots$
$Here,t_1=\sqrt{3},t_2=2\sqrt{3},t_3=3\sqrt{3}and{t}_4=4\sqrt{3}$
$t_2-t_1=2\sqrt{3}-\sqrt{3}=\sqrt{3}$
$t_3-t_2=3\sqrt{3}-2\sqrt{3}=\sqrt{3}$
$t_4-t_3=4\sqrt{3}-3\sqrt{3}=\sqrt{3}$
Clearly, the difference between successive terms is same.
Therefore, given list of numbers form an AP.