Answer:
[tex]a_n=97-n[/tex]
Step-by-step explanation:
Given:
[tex]h(1)=96\\ \\h(n)=h(n-1)-1[/tex]
Find first terms:
[tex]h(1)=96\\ \\h(2)=h(2-1)-1=h(1)-1=96-1=95\\ \\h(3)=h(3-1)-1=h(2)-1=95-1=94\\ \\h(4)=h(4-1)-1=h(3)-1=94-1=93\\ \\....[/tex]
In this arithmatic sequence, each next term is 1 less than the previous term.
The general explicit formula is
[tex]a_n=a_1+(n-1)d[/tex]
In your case,
[tex]a_1=96\ \text{ First term}\\ \\d=-1\ \text{ Common difference}[/tex]
Then
[tex]a_n=96+(n-1)\cdot (-1)\\ \\a_n=96-(n-1)\\ \\a_n=96-n+1\\ \\a_n=97-n[/tex]
