Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Skill Practice - Page 814: 33

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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 $a_1=768\\a_2=-192\\a_3=48\\a_4=-12\\a_5=3\\a_6=-0.75$