Solution
We are given the arithmetic sequence
[tex]\begin{gathered} a_1=5 \\ a_n=a_{n-1}-4 \end{gathered}[/tex]
To find an explicit formula
[tex]\begin{gathered} First\text{ }Term=5 \\ a=5 \end{gathered}[/tex]
From the second recursive formula
[tex]\begin{gathered} a_n-a_{n-1}=-4 \\ Common\text{ }Difference=-4 \\ d=-4 \end{gathered}[/tex]
The nth term of an Arithmetic sequence is given by
[tex]\begin{gathered} a_n=a+(n-1)d \\ a_n=5+(n-1)(-4) \end{gathered}[/tex]
Therefore, the answer is
[tex]a_{n}=5+(n-1)(-4)[/tex]
