The n-th term of a geometric sequence is given by the formula:
[tex]\begin{gathered} U_n=a_1r^{n-1} \\ r=\text{ common ration} \\ a_1=\text{ first term} \end{gathered}[/tex]Given that:
[tex]\begin{gathered} a_2=64 \\ r=\frac{1}{4} \\ n=2 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} a_2=a_1(\frac{1}{4})^{2-1}=64 \\ a_1(\frac{1}{4})=64 \\ a_1=64\times4 \\ =256 \end{gathered}[/tex]Therefore, the rule for the nth term of the sequence is
[tex]\begin{gathered} U_n=a_1r^{n-1} \\ U_n=256_{}(\frac{1}{4})^{n-1} \end{gathered}[/tex]