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If the sum of the first n terms of a geometric series is given by S_n = (2)(−1+(−2)^n)

 

 find the 4th term of the series

 

Select one:

a. 30

b. −34

c. 48

d. 12

 Feb 21, 2019
 #1
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If you look at the generic Sum of a Geometric Series

Sn= a1(1-r^n)/(1-r)      and the equation you are given  (with some manipulation)

 

  a1 = -6           and    (1-r^n) / (1-r)  =   (1+2^n)/(1+2)         so r = -2

 

Because   -6 (1+2^n) / (1+2)  =

                  6 (-1 -2^n)/(1+2)

                  2 (-1-2^n)   

 

-6 * -2 *-2*-2 = 48

 Feb 21, 2019

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