Sum of a G.P. series is represented by the formula, Sn = a \(\frac{r^n - 1}{r-1}\) , when r>1.
‘Sn’ represents the sum of the G.P. series up to 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