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
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