Answer:
[tex]a_{n}[/tex] = - 4n + 6
Step-by-step explanation:
There is a common difference between consecutive terms of the sequence
- 2 - 2 = - 6 - (- 2) = - 10 - (- 6) = - 14 - (- 10) = - 4
This indicates the sequence is arithmetic with explicit formula
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 2 and d = - 4 , then
[tex]a_{n}[/tex] = 2 - 4(n - 1) = 2 - 4n + 4 = - 4n + 6
