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Answer 1 · 2017-11-24T11:52:57

Sum of the series is #1094 #

Geometric series is #S= {2 , -6 , 18 ,-54 , ..... 1458}#

First term is #a_1=2# , common ratio is # r = 18/-6=(-6)/2=-3#

#a_n= 1458 ; a_n= a_1*r^(n-1) or 1458= 2*(-3)^(n-1)# or

#(-3)^(n-1) =1458/2=729 ; (-3)^(n-1)= (-3)^6 :. n-1=6# or

#n=6+1=7 ; S_n=S_7= a_1* (r^n-1)/(r-1) # or

#S_7= 2* ((-3)^7-1)/(-3-1) =((-3)^7-1)/-2=1094 #

Sum of the series is #1094 # [Ans]