Respuesta :

Using the formula for the explicit rule: [tex]a_n=a_1*r^n^-^1[/tex]
You can find r: [tex]r= \frac{2nd term}{first term} = \frac{ \frac{4}{5} }{4}[/tex]
[tex]a_n=4( \frac{1}{5} )^n^-^1[/tex]

The explicit rule of given geometric sequence is,  [tex]a_{n}=4(1/5)^{n-1}[/tex]

In any geometric sequence, common ration would be equal.

Given sequence is,     4,  4/5, 4/25, 4/125,...

First term, [tex]a_{1}=4[/tex]

Common ratio,  [tex]r=\frac{4}{5}\div 4=\frac{4}{5} *\frac{1}{4}=\frac{1}{5}[/tex]

General term for geometric sequence,

                                   [tex]a_{n}=a_{1}r^{n-1}\\\\a_{n}=4*(\frac{1}{5} )^{n-1}[/tex]

Thus, The explicit rule of given geometric sequence is,  [tex]a_{n}=4(1/5)^{n-1}[/tex]

Learn more:

https://brainly.com/question/15978376