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 = 1

r = (ratio between the n term and n-1 term) 3 ÷ 1 = 3

n = 7 terms

$\therefore \mathrm{S}_{\mathrm{n}}=1 \frac{3^{7}-1}{3-1}$

$\Rightarrow \mathrm{S}_{\mathrm{n}}=\frac{2187-1}{3-1}$

$\Rightarrow \mathrm{S}_{\mathrm{n}}=\frac{2186}{2}$

$\Rightarrow \mathrm{S}_{\mathrm{n}}=1093$