\left\{ \begin{array} { l } { a \cdot ( 1 + q ) = 2 } \\ { a _ { 1 } ( 1 + q + q ^ { 2 } ) = - 6 } \end{array} \right.
Solve for a, q, a_1
a=\frac{2}{q+1}\text{, }q=-\frac{\sqrt{-3a_{1}^{2}-24a_{1}}}{2a_{1}}-\frac{1}{2}\text{, }a_{1}\in [-8,0)\text{; }a=\frac{2}{q+1}\text{, }q=\frac{\sqrt{-3a_{1}^{2}-24a_{1}}}{2a_{1}}-\frac{1}{2}\text{, }a_{1}\in [-8,-6)\cup (-6,0)
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