The next term of the A.P., $$\sqrt 7 ,$$ $$\sqrt {28} ,$$ $$\sqrt {63} ,$$ . . . . . .

Solution (By Examveda Team)

$$\eqalign{ & {\text{A}}{\text{.P}}{\text{.}}\,{\text{is}}\,\sqrt 7 ,\,\sqrt {28} ,\,\sqrt {63} ,\,...... \cr & \Rightarrow \sqrt 7 ,\,\sqrt {4 \times 7} ,\,\sqrt {9 \times 7} ,\,..... \cr & \Rightarrow \sqrt 7 ,\,2\sqrt 7 ,\,3\sqrt 7 ,...... \cr & \therefore Here\,\,a = \sqrt 7 \,{\text{and}} \cr & d = 2\sqrt 7 - \sqrt 7 = \sqrt 7 \cr & \therefore {\text{Next}}\,{\text{term}} = 4\sqrt 7 \cr & = \sqrt {\left( {16 \times 7} \right)} \cr & = \sqrt {112} \cr} $$