The product of $3$ numbers in $GP$ is $1000$. If $6$ and $7$ are added to the $2^{nd}$ and $3^{rd}$ terms respectively, the terms form an $AP.$ Find the $GP$.

Question

$\begin{array}{1 1} 4,10,25 \\ 25,10,4 \\ 5,10,20 \\ -5,10,-20 \end{array}$