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Which choice is the explicit formula for the following geometric sequence?0.5, -0.1, 0.02, -0.004, 0.0008, ...O A. an = -0.5(0,2)(n-1)B. an = 0.5(0.2)"C. an = 0.5(-0.2)(n-1)D. an = -0.5(0.3)(n-1)E. an = -0.5(-0.2) (n = 1)N

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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