Answer:
The recursive formula for the arithmetic sequence is given by:
[tex]a_n = a_{n-1} +d[/tex] for [tex]n\geq 2[/tex]
where, d is the common difference.
Given the sequence:
-16,-7,2,11...
This is a arithmetic sequence:
[tex]a_1 = -16[/tex] and d = 9
Since,
-7-(-16) = -7+6 = 9,
2-(-7) = 2+7 = 9,
11-2 = 9 and so on...
⇒ common difference(d) = 9
Substitute in [1] we have;
[tex]a_n = a_{n-1}+9[/tex] for [tex]n\geq 2[/tex]
Therefore, the recursive formula for this arithmetic sequence is,
[tex]a_1 = -16[/tex]
[tex]a_n = a_{n-1}+9[/tex] for [tex]n\geq 2[/tex]
