Question

$(3) \: (3 \sqrt{3)} \: \:( 9)$
are in GP then which term is 243

Answer 1

Here a= 3 and r= √3.

$n = a\times {r}^{n -1 }$
$n = 3 \times( {\sqrt{3}})^{n - 1}$
$243 = { \sqrt{3} }^{2} \times {\sqrt{3} }^{n - 1}$
${ \sqrt{3} }^{10} = { \sqrt{3} }^{n + 1}$
n+1 = 10 or n = 9