Answer:
[tex]a_{n}[/tex] = 10.5 - 3n
Step-by-step explanation:
The explicit rule for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
A recursive formula has the form
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d ( where d is the common difference )
Given
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 3 ⇒ d = - 3
Thus explicit rule with a₁ = 7.5 and d = - 3
[tex]a_{n}[/tex] = 7.5 - 3(n - 1) = 7.5 - 3n + 3 = 10.5 - 3n
