For the following geometric sequence find the recursive formula and the 5th term in the sequence. in your final answer, include all of your work. {-4, 12, -36, }

The nth term for the geometric sequence is given by:

where,

is the first term

r is the common ratio term

n is the number of terms.

Given the sequence:

-4, 12, -36,......

This is a geometric sequence with   and  

Since,

,

ans so on...

Substitute this in [1] we have;

Substitute n = 5 we have;

⇒

Recursive formula for the geometric sequence is given by:

Substitute the given values we have;

Therefore, the recursive formula and the 5th term in the sequence is,

;

3 1/3 x 2 3/5 = 8 2/3

step-by-step explanation:

just multiply the first number by the second number to get your answer.