Answer:
\(a_n = (-3) *a_{n-1} \\ a_5 = -324\)
Step-by-step explanation:
Let's remember the definition of geometric sequence:
Each term is found by multiplying the previous term by a constant.
We need to find out that constant. As it's always the same, we just need to divide the second term by the first one to get it.
\(12/-4 = -3\)
The recursive formula will be:
\(a_1 = -4 \\ a_n = (-3) *a_{n-1}\)
With this, to find the 5th term in the sequence we need the fourth one first
\(a_4 = (-3) *a_3 = (-3) *(-36) = 108\\ a_5 = (-3) *a_4 = (-3) *108 = -324\)
\(a_5 = -324\)
