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Sagot :
The nth term of a geomeric series having first term 'a' and the common ratio 'r' is given by,
[tex]a_n=a\cdot r^{n-1}[/tex]Now, consider the given geometric sequence,
[tex]0.5,-0.1,0.02,-0.004,0.0008,\ldots\ldots[/tex]Observe that the first term of the sequence is 0.5,
[tex]a=0.5[/tex]The common difference is calculated as,
[tex]\begin{gathered} r=\frac{a_2}{a_{}} \\ r=\frac{-0.1}{0.5} \\ r=-0.2 \end{gathered}[/tex]Substitute the values,
[tex]a_n=(0.5)(-0.2)^{n-1}[/tex]This expression is given in option C. Therefore, option C is the correct choice.
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