Answer:
[tex]a_n=3n-12[/tex]
Step-by-step explanation:
We are given the recursive formula:
[tex]a_n=a_{n-1}-4, a_1=15[/tex]
This is the recursive formula for an arithmetic sequence.
The explicit formula for an arithmetic sequence is given by:
[tex]a_n=a_1 + d({n-1} )[/tex]
Where d=3 is the common difference.
We plug in this values to get:
[tex]a_n=15 + 3({n-1} )[/tex]
We now expand and simplify to get:
[tex]a_n=15 + 3n-3[/tex]
We simplify to obtain:
[tex]a_n= 3n-12[/tex]
