Answer:
[tex]\begin{gathered} a_n=a_{n-1}+4x \\ a_1=5x \end{gathered}[/tex]Explanation:
Given the sequence defined by the explicit formula:
[tex]a_n=x+4xn[/tex]When n=1:
[tex]\begin{gathered} a_1=x+4x(1)=5x \\ a_1=5x \end{gathered}[/tex]When n=2
[tex]\begin{gathered} a_2=x+4x(2)=9x \\ a_2=9x \end{gathered}[/tex]When n=3
[tex]\begin{gathered} a_3=x+4x(3)=13x \\ a_3=13x \end{gathered}[/tex]We observe that:
[tex]\begin{gathered} 9x-5x=4x \\ 13x-9x=4x \end{gathered}[/tex]This means that to get the next term, we add 4x to the previous term.
Therefore, a recursive formula for the sequence will be:
[tex]\begin{gathered} a_n=a_{n-1}+4x \\ a_1=5x \end{gathered}[/tex]