Question

Write the next term of the $AP:\sqrt{2},\sqrt{8},\sqrt{18},...$

Answer 1

Given Sequence are in $AP:\sqrt{2},\sqrt{8},\sqrt{18},....$​​​​

⇒ $\sqrt{2},\sqrt{4\times 2},\sqrt{9\times 2},\dots$

⇒ $\sqrt{2},2\sqrt{2},3\sqrt{2},,\dots \dots$​​​​​​​

common difference is $\sqrt{2}$​​​​​​​.

∴ Next terms $4\sqrt{2},5\sqrt{2},6\sqrt{2}$​​​​​​​ and so on.