Answer
See below
Work Step by Step
The sequence is geometric with first term $a_4=-12$ and common ratio $r=-\frac{1}{4}$. We obtain: $$a_n=a_5r^{n-5}\\a_4=a_1r^3\\-12=a_1\times(-\frac{1}{4})^3\\-\frac{1}{64}a_1=-12\\a_1=768$$
So, a rule for the nth term is: $$a_n=768\times(-\frac{1}{4})^{n-1}$$
The first 6 terms are $a_1=768\\a_2=-192\\a_3=48\\a_4=-12\\a_5=3\\a_6=-0.75$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/5ac1810c-dbdd-4ae2-b80c-4c799dc65d8a/steps_image/small_1636048094.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20241221%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20241221T144353Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=cf05c282b6f7753aef025f5da31f8c50e9a17d6b5edec6d0d20fe4ef81607649)