For the following $G . P . s,$ find $S_{n}$
$2, 6, 18, 54, . . .$

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Solution

For geometric progression,
$S_{n} = \frac{a_{1} (1 - r^{n})}{1 - r}, r \neq 1$
$a_{1} : 1 s t$ term of series
r : common ratio $e x; \frac{a_{2}}{a_{1}}, \frac{a_{3}}{a_{2}}$
n : $n^{t h}$ term.
for above example ;
$a_{1} = 2, r = \frac{a_{2}}{a_{1}} = \frac{6}{2} = 3$
$S_{n} = \frac{2 (1 - 3^{n})}{1 - 3}$
$= \frac{2 (1 - 3^{n})}{- 2} = - (1 - 3^{n})$

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