Answer:
[tex]a_{n}[/tex] = 3n - 8
Step-by-step explanation:
Note the common difference d between consecutive terms, that is
d = - 2 - (- 5) = 1 - (- 2) = 4 - 1 = 7 - 4 = 3
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 = - 5 and d = 3, thus
[tex]a_{n}[/tex] = - 5 + 3(n - 1) = - 5 + 3n - 3 = 3n - 8
