Given #-\frac { 3} { 2} ,3,- 6,12#, what is the sum of the first 13 terms in this series?

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Answer 1 · 2017-07-02T02:41:12

#-8193/2#

This is a geometric series, and we can see that the common ratio is #-2#:

#-3/2 xx (-2) = 3#

#3 xx (-2) = -6#

#-6 xx (-2) = 12#

The formula for the first #n# terms of a geometric sequence with first term #a_0# and ratio #r# is:

#S_n = (a_0(1-r^n))/(1-r)#

For this case, #r=-2#, #a_0=-3/2#, and #n=13#.

#S_13 = (-3/2(1-(-2)^13))/(1-(-2))#

#= (-3/2(1+2^13))/(1+2)#

#= (-3/2(8193))/3#

#= -8193/2#

Final Answer