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, }

We have a geometric sequence > {-4, 12, -36, ...}

the formula is a(r)^(n-1)

a >a is the first term > -4
r > is the common ratio > 12/(-4)=(-36/12)=-3
n > is the number of terms

The fifth term is -4[(-3)^(5-1)]=-4[(81]=-324

the answer is -324

First you need to identify the common ratio:

r = 

where r is the common ratio
           is any term in the sequence
          is the term preceding

In your case the common ratio will be 
  12/-4 = -3
The recursive formula of a geometric sequence is:

An =  x r
Where : An is the nth term
              is the erm preceding the nth term
             r = common ratio

For this case it is:
An =  x -3

Now let us use this formula to find the 5th term:

= x -3
= x -3

Since you do not know the 4th term, you can use that by using our reclusive formula:

= x -3
= x -3
= x -3
=

Now that you know your fourth term, you can use the same formula:

= x -3
= x -3
= x -3
=