The geometric series is [ -2,(-1/2),(-1/8),(1/32)]. Then option C is correct.
What is a geometric sequence?
A geometric sequence is a sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
The formula for the geometric series is,
[tex]f(n) =a(r)^{n-1}[/tex]
The first term is -2 and the common ratio is (-1/4). The next three terms will be calculated as:-
[tex]f(2)= ar^{(2-1)}=(-2)(\dfrac{-1}{4})^1=\dfrac{1}{2}[/tex]
[tex]f(3)= ar^{(3-1)}=(-2)(\dfrac{-1}{4})^2=\dfrac{-2}{16}=\dfrac{-1}{8}[/tex]
[tex]f(4)= ar^{(4-1)}=(-2)(\dfrac{-1}{4})^3=\dfrac{-2}{-64}=\dfrac{1}{32}[/tex]
Hence, the correct option is C.
Learn more about the geometric sequence here;
brainly.com/question/1509142
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