Odpowiedź:
[tex]q = -\frac{1}{2}[/tex]
[tex]a_8 = -\frac{3}{4}[/tex]
Szczegółowe wyjaśnienie:
[tex]S_n = a_1 \cdot \frac{1-q^{n}}{1-q}\\[/tex]
[tex]66 = S_5 = a_1 \cdot \frac{1-q^{5}}{1-q}\\[/tex]
[tex]-33 = S_6 - S_1 = a_1 \cdot \frac{1-q^{6}}{1-q} - a_1 \cdot \frac{1-q}{1-q} = a_1 \cdot \frac{-q^{6}+q}{1-q} = a_1 \cdot \frac{q\cdot(1-q^{5})}{1-q}\\[/tex]
[tex]-\frac{1}{2} = -\frac{33}{66} = \frac{S_6 - S_1}{S_5} = \frac{a_1 \cdot \frac{q\cdot(1-q^{5})}{1-q}}{a_1 \cdot \frac{1-q^{5}}{1-q}} = q\\[/tex]
[tex]a_1 = S_5 \cdot \frac{1-q}{1-q^{5}} = 66 \cdot \frac {1-(-\frac{1}{2})}{1-(-\frac{1}{2})^{5}} = 96\\[/tex]
[tex]a_8 = a_1 \cdot q^{7} = 96 \cdot (-\frac{1}{128}) = -\frac{3}{4}\\[/tex]
