Find the sum of the GP :
1 + 3 + 9 + 27 + …. To 7 terms
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
$\therefore \mathrm{S}_{\mathrm{n}}=1 \frac{3^{7}-1}{3-1}$
$\Rightarrow \mathrm{S}_{\mathrm{n}}=\frac{2187-1}{3-1}$
$\Rightarrow \mathrm{S}_{\mathrm{n}}=\frac{2186}{2}$
$\Rightarrow \mathrm{S}_{\mathrm{n}}=1093$
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