Find a formula for Sn, the sum of the first n terms of the following geometric sequence. Help?

$\sqrt{3} + 3 + 3 \sqrt{3} + 9. . .$ using the formula $S n = u 1 \frac{1 - {r}^{n}}{1 - r}$

Mar 18, 2017

${S}_{n} = \sqrt{3} \cdot \frac{1 - {\left(\sqrt{3}\right)}^{n}}{1 - \sqrt{3}}$

Explanation:

${u}_{1} = \sqrt{3}$

$r = \sqrt{3}$

and you are told:
$\textcolor{w h i t e}{\text{XXX}} {S}_{n} = {u}_{1} \cdot \frac{1 - {r}^{n}}{1 - r}$

so, it's just a matter of substitution.