Find the sum of the GP :

Sum of a G.P. series is represented by the formula $\mathrm{S}_{\mathrm{n}}=\mathrm{a} \frac{\mathrm{r}^{\mathrm{n}}-1}{\mathrm{r}-1}$

when r>1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.

Here,

$a=\frac{2}{9}$

$r=($ ratio between the $n$ term and $n-1$ term $)-\frac{1}{3} \div \frac{2}{9}=-\frac{3}{2}=1.5$

n = 6 terms

$\therefore \mathrm{S}_{\mathrm{n}}=\frac{2}{9} \times \frac{1.5^{6}-1}{1.5-1}$

$\Rightarrow \mathrm{S}_{\mathrm{n}}=\frac{2}{9} \times \frac{10.39}{0.5}$

$\therefore \mathrm{S}_{\mathrm{n}}=4.62$