Answer:
[tex]a_{n}[/tex] = - 5n - 2
Step-by-step explanation:
There is a common difference between consecutive terms, that is
- 12 - (- 7) = - 17 - (- 12) = - 5
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 7 and d = - 5, then
[tex]a_{n}[/tex] = - 7 - 5(n - 1) = - 7 - 5n + 5 = - 5n - 2
