The next $\left(4^{ ext {th }} ight)$ term of the A.P. $\sqrt{18}, \sqrt{50}, \sqrt{98}, \ldots$.

Question

The next $\left(4^{	ext {th }}ight)$ term of the A.P. $\sqrt{18}, \sqrt{50}, \sqrt{98}, \ldots$. is:\

Professor PC Thomas Classes · Answer

(c) : Given A.P. $\sqrt{18}, \sqrt{50}, \sqrt{98}, \ldots \ldots$. can be written as $3 \sqrt{2}, 5 \sqrt{2}, 7 \sqrt{2}, \ldots \ldots$\ Here, $a=3 \sqrt{2}, d=5 \sqrt{2}-3 \sqrt{2}=2 \sqrt{2}$\ $	herefore \quad a_{4}=a+3 d$ $$ \left(\because a_{n}=a+(n-1) dight) $$ $\Rightarrow a_{4}=3 \sqrt{2}+3 	imes 2 \sqrt{2}$\ $\Rightarrow a_{4}=3 \sqrt{2}+6 \sqrt{2}=9 \sqrt{2}=\sqrt{162}$\