Solution:
The general formula of a geometric sequence is expressed as
[tex]\begin{gathered} a_n=a_1\times r^{n-1} \\ where \\ a_1\Rightarrow first\text{ term of the sequence} \\ r\Rightarrow common\text{ ratio} \end{gathered}[/tex]
Given the geometric sequence:
[tex]4,\text{ 20, 100, 500, . . .}[/tex]
where
[tex]\begin{gathered} a_1=4 \\ r=\frac{a_2}{a_1}=\frac{20}{4}=5 \end{gathered}[/tex]
By substitution, we have
[tex]a_n=4\times5^{(n-1)}[/tex]
Hence, the formula of the geometric sequence is
[tex]a_n=4\cdot5^{n-1}[/tex]
The correct option is'
