Answer:
[tex]a_{n}[/tex] = - 4 × [tex]2^{n-1}[/tex]
Step-by-step explanation:
Note there is a common ratio between consecutive terms in the sequence.
r = - 8 ÷ - 4 = - 16 ÷ - 8 = - 32 ÷ - 16 = 2
This indicates that the sequence is geometric with n th term
[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Here a = - 4 and r = 2, thus
[tex]a_{n}[/tex] = - 4 [tex](2)^{n-1}[/tex] ← explicit rule
