Answer:
[tex]a_{n}[/tex] = - 4[tex](4)^{n-1}[/tex]
Step-by-step explanation:
Note the common ratio r between consecutive terms in the sequence, that is
- 16 ÷ - 4 = - 64 ÷ - 16 = - 256 ÷ - 64 = 4
This indicates the sequence is geometric with n th term ( explicit formula )
[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 = 4, thus
[tex]a_{n}[/tex] = - 4 [tex](4)^{n-1}[/tex] ← explicit formula
