Question

find out the next term of the A.P.√7,√28,√63

Answer 1

a = √7

d = √28 - √7


√28 can be written as
$\sqrt{28} = \sqrt{4 \times 7} \\ \\ = > \sqrt{4} \times \sqrt{7} \\ \\ = > 2 \sqrt{7}$

So, d = √28 - √7

=> d = 2√7 - √7

=> d = √7


Hence, Next term = √63 + d

√63 can be written as

$\sqrt{63} = \sqrt{9 \times7 } \\ \\ = 3 \sqrt{7}$

Next term = 3√7 + √7

= 4√7

=>
$4 \sqrt{7} = \sqrt{16} \times \sqrt{7} \\ \\ = \sqrt{112}$


Answer :- √112

Answer 2

$\sqrt{7}, \sqrt{28}, \sqrt{63}....$


If you observe clearly,

$\sqrt{28} = \sqrt{7 \times 4} = 2 \sqrt{7}$
And
$\sqrt{63} = \sqrt{7 \times 9} = 3 \sqrt{7}$
This makes an AP with First term $a=\sqrt{7}$ and the common difference $d=\sqrt{7}$

Thus the next term of this AP is

$3 \sqrt{7} + \sqrt{7} \\ = 4 \sqrt{7} \\ = \sqrt{112}$