If  $a, b, c$ are in A.P. and $a^2, b^2, c^2$ are in G.P., then the common ratio of G.P. is ___

$$\begin{gathered} 2b=a+c\to \left(1\right) \\ {b}^4=a^2{c}^2 \\ let\frac{b^2}{a^2}=r \\ \Rightarrow b^2=r{a}^2 \\ {c}^2=r^2{a}^2 \\ Now, \\ from\left(1\right),4b^2=a^2+c^2+2ac \\ 4r{a}^2=a^2+r^2{a}^2+2a^{2}r \\ \Rightarrow r^2-2r+1=0 \\ \Rightarrow {(r-1)}^2=0 \\ \Rightarrow r=1 \end{gathered}$$