Question

What is the recursive rule for the sequence 1, −6, 36, −216, ... ? an=6⋅an−1 , a1=1 an=−6⋅an−1 , a1=1 an=−16⋅an−1 , a1=1 an=16⋅an−1 , a1=1

Answer 1

Answer:

Option 2) $a_n = -6(a_{n-1})$            

Step-by-step explanation:

We are given the following sequence in the question:

$1, -6, 36, -216, ...$

We have to find the recursive relation for the sequence.

$a_1 =1\\a_2 = -6 = -6(1) = -6(a_1)\\a_3 = 36 = -6(-6) = -6(a_2)\\a_4 = -216 = -6(36) = -6(a_3)$

Thus, continuing in the following manner, we get,

$a_n = -6(a_{n-1})$

Thus, the recursive rule is given by

Option 2) $a_n = -6(a_{n-1})$