Find the sum of the GP :


Find the sum of the GP :

$1+\sqrt{3}+3+3 \sqrt{3}+\ldots . .$ to 10 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.


a = 1

$r=($ ratio between the $n$ term and $n-1$ term $) \sqrt{3} \div 1=\sqrt{3}=1.732$

n = 10 terms

$\therefore \mathrm{S}_{\mathrm{n}}=1 \cdot \frac{\sqrt{3}^{10}-1}{\sqrt{3}-1}$

$\Rightarrow \mathrm{S}_{\mathrm{n}}=\frac{1.732^{10}-1}{1.732-1}$

$\Rightarrow \mathrm{S}_{\mathrm{n}}=\frac{242.929-1}{0.732}$

$\Rightarrow \mathrm{S}_{\mathrm{n}}=\frac{241.929}{0.732}$

$\Rightarrow \mathrm{S}_{\mathrm{n}}=330.504$


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