Question

Question 4 (xii)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xii) $\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32}\dots \dots$

Answer 1

(xii) $\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32}\dots \dots$
Here,
$\sqrt{2}$

$\sqrt{8}=2\sqrt{2}$

$\sqrt{18}=3\sqrt{2}$

$\sqrt{32}=4\sqrt{2}$

Now, $\sqrt{8}-\sqrt{2}=\sqrt{18}-\sqrt{8}=\sqrt{32}-\sqrt{18}=\sqrt{2}$

So, the above terms are in AP

Common difference = $\sqrt{2}$

Three more terms are $\sqrt{50},\sqrt{72}$ and $\sqrt{98}$