What is the recursive formula for the geometric sequence with this explicit formula an=9*(-1/3)^(n-1)

a_0 = -27

a_n = a_(n-1) * (-1/3)

Step-by-step explanation:

First evaluate given formula at n=0 and specify that as starting value

Then find how to get from n-1 to n by comparing two values. In this case the next value is formed by multiplying by -1/3.

Step-by-step explanation:

The explicit formula for the geometric sequence is given by:

where,

is the first term

r is the common ratio to the following terms.

As per the statement:

Given the explicit formula for geometric sequence:

On comparing with [1] we have;

and

The recursive formula for geometric sequence is given by:

Substitute the given values we have;

Therefore, the recursive formula for the geometric sequence is,

36 is the final answer! : )