Question

Write the next term of the $AP:\sqrt{8},\sqrt{18},\sqrt{32},....$

Answer 1

Given Sequence are in $AP:\sqrt{8},\sqrt{18},\sqrt{32},....$​​​​

⇒ $\sqrt{4\times 2},\sqrt{9\times 2},\sqrt{16\times 2},\dots$

⇒ $2\sqrt{2},3\sqrt{2},4\sqrt{2},\dots \dots$​​​​​​​

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

∴ Next terms $5\sqrt{2},6\sqrt{2},7\sqrt{2}$​​​​​​​ and so on.