What is the sum of the first 7 terms of the sequence #10xx(-2)^(i-1)# ?

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Answer 1 · 2016-07-02T05:20:00

430

The sum of the first n terms of a geometric series with first term #a_1# and common ratio r is given by:

#sum_(i=1)^n = [a_1(1-r^n)]/(1-r)#

In this example, #n=7, a_1 = 10# and #r=-2#

Hence, #sum_(i=1)^7 = (10*(1-(-2)^7))/(1-(-2))#

#= (10*(1-(-128)))/3#

#=1290/3 = 430#