Correct option is (D) 9
Given G.P. is \(3, 3 \sqrt3,9,.......\)
\(\therefore a_1=3,a_2=3\sqrt3\)
\(\therefore\) Common ratio is r \(=\frac{a_2}{a_1}\)
\(=\frac{3\sqrt3}3=\sqrt3\)
Let \(a_n=243\)
\(\therefore ar^{n-1}=243\) \((\because a_n=ar^{n-1})\)
\(\Rightarrow3(\sqrt3)^{n-1}=243\)
\(\Rightarrow3\frac{n-1}2=\frac{243}3\)
\(=81=3^4\)
\(\Rightarrow\frac{n-1}2=4\)
\(\Rightarrow n-1=8\)
\(\Rightarrow n=8+1=9\)
Hence, \(9^{th}\) term of given G.P. equals to 243.
