Answer:
Option 2) [tex]a_n = -6(a_{n-1})[/tex]
Step-by-step explanation:
We are given the following sequence in the question:
[tex]1, -6, 36, -216, ...[/tex]
We have to find the recursive relation for the sequence.
[tex]a_1 =1\\a_2 = -6 = -6(1) = -6(a_1)\\a_3 = 36 = -6(-6) = -6(a_2)\\a_4 = -216 = -6(36) = -6(a_3)[/tex]
Thus, continuing in the following manner, we get,
[tex]a_n = -6(a_{n-1})[/tex]
Thus, the recursive rule is given by
Option 2) [tex]a_n = -6(a_{n-1})[/tex]
