Identify the indicated sum for the geometric series. S9 for 3 − 6 + 12 − 24 + ..... ?

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Answer 1 · 2018-06-18T15:34:02

$S_{9} = 513$ $S_9=513$

Here,

$3,(-6),12,(-24),...$ is the geometric sequn.

$where, 1^(st) term=a_1=3 and$ common ratio

$r= (-6)/3=12/(-6)=(-24)/12=-2$ and $S_9= ?=>n=9$

We know that,

$"The sum of first n term of Geometric series is :"$

$color(blue)(S_n=(a_1(r^n-1))/(r-1)$

Putting , $a_1=3, r=-2 and n=9$

$S_9=(3[(-2)^9-1])/((-2)-1)$

$:.S_9=(3[-512-1])/(-3)$

$=>S_9=(3(-513))/(-3)$

$=>S_9=513$