Problem

Find the $9^{th}$ partial sum of the geometric sequence $a_{n} = 3^{n - 1}$ .

Answer

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Answer

$S_{9} = - \frac{3^{8} - 1}{2}$

Steps

Step 1 ： $S_{9} = \frac{a_{1} (1 - r^{9})}{1 - r}$

Step 2 ： $S_{9} = \frac{3^{1 - 1} (1 - 3^{9 - 1})}{1 - 3}$

Step 3 ： $S_{9} = - \frac{3^{8} - 1}{2}$

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