If $a, b, c$ are in $AP$ and $a^2,b^2,c^2$ are in $HP$, how are $a, b$ and $\large\frac{-c}{2}$ related?

Question

$\begin{array}{1 1} Not\;related \\a, b, \frac{-c}{2}\; are \infty \\a, b, \frac{-c}{2} are\; in\; AP \\ a, b, \frac{-c}{2}\; are\; in\; GP \end{array}$