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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]