If $x,2x+2,3x+3$  are in G.P., then $5x,10x+10,15x+15$  forms

$\frac{2\left(x+1\right)}{x}=\frac{3\left(x+1\right)}{2\left(x+1\right)}$

$4\left(x+1\right)=3x$

$4x+4=3x$

$x=-4$

$\therefore -4,-6,-9$  are in G.P

Take $5x,10x+10,15x+15$

$=5\left(-4\right),10\left(-4\right)+10,15\left(-4\right)+15$

$=-20,-30,-45$

Consider $\frac{-30}{-20}=\frac{3}{2}$

$\frac{-45}{-30}=\frac{3}{2}$

$\therefore 5x,10x+10,15x+15$  is in G.P.