sssooss!!!

a)
$\displaystyle  \begin{array}{{>{\displaystyle}l}}
u_{4} =u_{1} *q^{3}\\
u_{2} =u_{1} *q\\
u_{5} =u_{1} *q^{4}\\
u_{3} =u_{1} *q^{2}\\
u_{4} +u_{2} =60=u_{1} *q^{3} +u_{1} *q\rightarrow u_{1} *q*\left( q^{2} +1\right) =60\\
u_{5} +u_{3} =180=u_{1} *q^{4} +u_{1} *q^{2}\rightarrow u_{1} *q^{2} *\left( q^{2} +1\right) =180\\
\rightarrow q=3\rightarrow u_{1} =2\\
\end{array}$
b)
$\displaystyle  \begin{array}{{>{\displaystyle}l}}
u_{7} =u_{1} *q^{6}\\
u_{3} =u_{1} *q^{2}\\
u_{5} =u_{1} *q^{4}\\
\rightarrow u_{7} -u_{1} =u_{1} *q^{6} -u_{1} =728\rightarrow u_{1} *\left( q^{6} -1\right) =728\\
\ \ \ \ \ \ u_{1} +u_{3} +u_{5} =u_{1} +u_{1} *q^{2} +u_{1} *q^{4} =91\rightarrow u_{1} *\left( q^{4} +q^{2} 2+1\right) =91\\
\rightarrow \frac{q^{6} -1}{q^{4} +q^{2} +1} =8\rightarrow \frac{\left( q^{2} -1\right) *\left( q^{4} +q^{2} +1\right)}{q^{4} +q^{2} +1} =8\rightarrow q^{2} -1=8\leftrightarrow q\in \{3;-3\}\\
\end{array}$