Answer:
![\begin{gathered} a_n=a_(n-1)+4x \\ a_1=5x \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/5yaxe9ef8cerwxmcpq09.png)
Step-by-step explanation:
Given the sequence defined by the explicit formula:
![a_n=x+4xn](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/cj3l6pgi6xlfa3s0hdzl.png)
When n=1:
![\begin{gathered} a_1=x+4x(1)=5x \\ a_1=5x \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/kss601ptbxn53w05on8z.png)
When n=2
![\begin{gathered} a_2=x+4x(2)=9x \\ a_2=9x \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/qenkgfivykbiv1lydial.png)
When n=3
![\begin{gathered} a_3=x+4x(3)=13x \\ a_3=13x \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/sshxvzm573o2cxa71bsj.png)
We observe that:
![\begin{gathered} 9x-5x=4x \\ 13x-9x=4x \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/jza1aloticzcm7l5zdx2.png)
This means that to get the next term, we add 4x to the previous term.
Therefore, a recursive formula for the sequence will be:
![\begin{gathered} a_n=a_(n-1)+4x \\ a_1=5x \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/5yaxe9ef8cerwxmcpq09.png)