If the 10th term of the sequence √3, \(\sqrt{12}\) , \(\sqrt{27}\)

1.	If the 10th term of the sequence √3, \(\sqrt{12}\) , \(\sqrt{27}\)……………..is \(\sqrt{3n^2}\) then the value of n/2 is ……………….. A) 3 B) √3 C) 5 D) √5
Answer» Correct option is (C) 5 Given sequence is \(\sqrt3 ,\sqrt{12} ,\sqrt{27},........\) \(\Rightarrow\sqrt{3},\sqrt{4\times3},\sqrt{9\times3},.....\) is the given sequence \(\Rightarrow\) \(\sqrt3,2\sqrt{3},3\sqrt{3},......\) is the given sequence \(\because\) \(1^{st}\) term of sequence \(=\sqrt3\) \(2^{nd}\) term of sequence \(=2\sqrt3\) \(3^{rd}\) term of sequence \(=3\sqrt3\) \(\vdots\) \(10^{th}\) term of sequence \(=10\sqrt3=\sqrt{3\times10^2}\) \(\therefore n=10\) (By comparing \(\sqrt{3n^2}\) with \(\sqrt{3\times10^2})\) \(\Rightarrow\) \(\frac{n}{2}=\frac{10}{2}=5\) Correct option is C) 5

If the 10th term of the sequence √3, \(\sqrt{12}\) , \(\sqrt{27}\)……………..is \(\sqrt{3n^2}\) then the value of n/2 is ……………….. A) 3 B) √3 C) 5 D) √5

Answer»

Correct option is (C) 5

Given sequence is \(\sqrt3 ,\sqrt{12} ,\sqrt{27},........\)

\(\Rightarrow\sqrt{3},\sqrt{4\times3},\sqrt{9\times3},.....\) is the given sequence

\(\Rightarrow\) \(\sqrt3,2\sqrt{3},3\sqrt{3},......\) is the given sequence

\(\because\) \(1^{st}\) term of sequence \(=\sqrt3\)

\(2^{nd}\) term of sequence \(=2\sqrt3\)

\(3^{rd}\) term of sequence \(=3\sqrt3\)

\(\vdots\)

\(10^{th}\) term of sequence \(=10\sqrt3=\sqrt{3\times10^2}\)

\(\therefore n=10\) (By comparing \(\sqrt{3n^2}\) with \(\sqrt{3\times10^2})\)

\(\Rightarrow\) \(\frac{n}{2}=\frac{10}{2}=5\)

Correct option is C) 5