Question

What is the next term of the AP $\sqrt{2},\sqrt{8},\sqrt{18},...?$
(a) $\sqrt{24}$
(b) $\sqrt{28}$
(c) $\sqrt{30}$
(d) $\sqrt{32}$

Answer 1

(d) $\sqrt{32}$32−−√
$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{AP}\mathrm{is}\sqrt{2},\sqrt{8},\sqrt{18},... \\ \mathrm{On}\mathrm{simplifying}\mathrm{the}\mathrm{terms},\mathrm{we}\mathrm{get}: \\ \sqrt{2},2\sqrt{2},3\sqrt{2,}... \\ \mathrm{Here},a=\sqrt{2}\mathrm{and}d=(2\sqrt{2}-\sqrt{2})=\sqrt{2} \\ \therefore \mathrm{Next}\mathrm{term},{\mathrm{T}}_4=a+3d=\sqrt{2}+3\sqrt{2}=4\sqrt{2}=\sqrt{32} \end{gathered}$$