Answer:
[tex]a_{n}[/tex] = - 95n
Step-by-step explanation:
Note the difference between consecutive terms in the sequence is constant
- 190 - (- 95) = - 190 + 95 = - 95
- 285 - (- 190) = - 285 + 190 = - 95
- 380 - (- 285) = - 380 + 285 = - 95
This indicates that the terms are an arithmetic sequence 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 = - 95 and d = - 95, thus
[tex]a_{n}[/tex] = - 95 - 95(n - 1) = - 95 - 95n + 95 = - 95n
