Verified Answer :

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

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

In any geometric sequence, common ration would be equal.

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

First term, \(a_{1}=4\)

Common ratio,  \(r=\frac{4}{5}\div 4=\frac{4}{5} *\frac{1}{4}=\frac{1}{5}\)

General term for geometric sequence,

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

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

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