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#

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#