​ Find the sum of the GP : 2/9 - 1/3 - 3/4 +. . .. To 6 terms ​

Question

Find the sum of the GP:
\(\frac{2}{9} - \frac{1}{3} - \frac{1}{2} - \frac{3}{4}\)+. . .. To 6 terms

Answer 1

Sum of a G.P. series is represented by the formula, S_n = a \(\frac{r^n - 1}{r-1}\) , when r>1. 

‘S_n’ represents the sum of the G.P. series up to n^th 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