Question

$\sqrt{3},\frac{1}{\left(\sqrt{3}\right)},\frac{1}{3\left(\sqrt{3}\right)}.....$
The ${19}^{\text{th}}$ term of the above sequence is .

Answer 1

In the given sequence,
$\frac{t_2}{t_1}=\frac{\frac{1}{\sqrt{3}}}{\sqrt{3}}=\frac{1}{3}.$
$\text{Common ratio,}r=\frac{1}{3}$
and
$\text{first term,}a=\sqrt{3}$
$\text{Now,}{a}_{19}=a{r}^{19-1}.$
$=\sqrt{3}\times {\left(\frac{1}{3}\right)}^{18}=\frac{\sqrt{3}}{3^{18}}$