Question

Which term of the G.P:
$-10,\frac{5}{\sqrt{3}},-\frac{5}{6},....$ is $-\frac{5}{72}$?

Answer 1

$-10,\frac{5}{\sqrt{3}},\frac{-5}{6}$

$n^{th}$ term of a GP is $a{r}^{n-1}$

$a=-10$

$r=\frac{5}{\sqrt{3}}\times \frac{-1}{10}=\frac{-1}{2\sqrt{3}}$

Given $n^{th}$ term $=\frac{-5}{72}$

$-10\times {\left(\frac{-1}{2\sqrt{3}}\right)}^{n-1}=\frac{-5}{72}$

${\left(\frac{-1}{2\sqrt{3}}\right)}^{n-1}=\frac{1}{144}$

${\left(\frac{-1}{2\sqrt{3}}\right)}^{n-1}={\left(\frac{-1}{2\sqrt{3}}\right)}^4$

$n-1=4$

$\therefore n=5$