Solve frac{a_{5}+a_{8}}{a_{2}+a_{5}}=q^3

$$\frac { a _ { 5 } + a _ { 8 } } { a _ { 2 } + a _ { 5 } } = q ^ { 3 }$$

Solve for a_2

$$\left\{\begin{matrix}a_{2}=\frac{a_{8}+a_{5}-a_{5}q^{3}}{q^{3}}\text{, }&a_{5}\neq -a_{8}\text{ and }q\neq 0\\a_{2}\neq -a_{5}\text{, }&q=0\text{ and }a_{5}=-a_{8}\end{matrix}\right.$$

Solve for a_5

$$\left\{\begin{matrix}a_{5}=-\frac{a_{8}-a_{2}q^{3}}{1-q^{3}}\text{, }&a_{8}\neq a_{2}\text{ and }q\neq 1\\a_{5}\neq -a_{8}\text{, }&a_{8}=a_{2}\text{ and }q=1\end{matrix}\right.$$