[tex]\displaystyle\bf\\4)\\\\b_{1} =8\\\\q=-\frac{1}{2} \\\\b_{n} =\frac{1}{32} \\\\n=?\\\\\\b_{n} =b_{1} \cdot q^{n-1} \\\\\\q^{n-1} =b_{n} : b_{1} =\frac{1}{32} :8= \frac{1}{2^{5} } \cdot \frac{1}{2^{3} }=\bigg(\frac{1}{2} \bigg)^{8} \\\\\\\bigg(\frac{1}{2} \bigg)^{n-1}=\bigg(\frac{1}{2} \bigg)^{8} \\\\\\n-1=8\\\\\\\boxed{\boxed{n=9}}[/tex]

[tex]\displaystyle\bf\\5)\\\\b_{1} =16\\\\b_{5} =81\\\\b_{5} =b_{1} \cdot q^{4} \\\\q^{4}=b_{5} : b_{1} =81:16 =\frac{81}{16} \\\\q_{1} =-1,5 \ \ , \ \ q_{2} =1,5\\\\1) \ q_{1} =-1,5\\\\b_{2} =b_{1} \cdot q=16\cdot (-1,5)=-24\\\\b_{3} =b_{2} \cdot q=-24\cdot (-1,5)=36\\\\b_{4} =b_{3} \cdot q=36\cdot(-1,5)=-54\\\\\\2) \ q_{1} =1,5\\\\b_{2} =b_{1} \cdot q=16\cdot 1,5=24\\\\b_{3} =b_{2} \cdot q=24\cdot 1,5=36\\\\b_{4} =b_{3} \cdot q=36\cdot 1,5=54[/tex]

[tex]\displaystyle\bf\\Otvet: 1) \ \ 16 \ , \ - 24 \ ; \ 36 \ ; \ -54 \ ; \ 81\\\\2) \ 16 \ ; \ 24 \ ; \ 36 \ ; \ 54 \ ; \ 81\\\\\\6)\\\\\left \{ {{b_{5} -b_{4}=36 } \atop {b_{5} -b_{3}=24 }} \right. \\\\\\\left \{ {{b_{1} q^{4} -b_{1} q^{3} =36} \atop {b_{1}q^{4} -b_{1} q^{2} =24 }} \right. \\\\\\:\left \{ {{b_{1} q^{3}\cdot (q-1)=36} \atop {b_{1} q^{2}\cdot(q-1)(q+1)=24 }} \right. \\---------------\\\\\frac{q}{q+1} =\frac{3}{2} \\\\\\3q+3=2q\\\\\\q=-3[/tex]

[tex]\displaystyle\bf\\b_{1} =\frac{36}{q^{3} \cdot(q-1)} =\frac{36}{-27\cdot(-4)} =\frac{1}{3} \\\\\\S_{7} =\frac{b_{1}\cdot(q^{7} -1) }{q-1} =\frac{\dfrac{1}{3} \cdot\bigg[(-3)^{7} -1\bigg]}{-3-1} =\frac{\dfrac{1}{3} \cdot(-2188)}{-4} =\frac{547}{3} =182\frac{1}{3}[/tex]