Answer:
[tex]f(n)=4^{n-1}[/tex]Explanation:
Given the sequence
[tex]1,4,16,64[/tex]We observe that the next term of the sequence is obtained by multiplying the previous term by 4.
This is an example of a geometric sequence.
The nth term of a geometric sequence is:
[tex]\begin{gathered} U_n=ar^{n-1} \\ \text{First term, a=1} \\ \text{Common ratio, r =4} \end{gathered}[/tex]Therefore, the nth term is:
[tex]U_n=1\times4^{n-1}[/tex]The explicit formula for the sequence is:
[tex]f(n)=4^{n-1}[/tex]
