Answer :
Notice that the common factor between the terms of the sequence is r = 4, then, a formula for the recursive function is:
[tex]\begin{gathered} a_n=a_1r^{n-1} \\ a_1=5 \\ r=4 \\ \Rightarrow a_n=5\cdot4^{n-1} \end{gathered}[/tex]and the recursive function can be found from this formula:
[tex]\begin{gathered} a_n=a_{n-1}\cdot r \\ \Rightarrow a_n=4a_{n-1} \end{gathered}[/tex]