Suppose a, b, c are in A.P. and a^2, 2 b^2, c^2 are in G.P. If a < b < c and a + b + c =1, then 9( a^2+ b^2+ c^2) is equal to ____.

Suppose $\displaystyle \mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P. and $\displaystyle \mathrm{a}^2, 2 \mathrm{~b}^2, \mathrm{c}^2$ are in G.P. If $\displaystyle \mathrm{a}<\mathrm{b}<\mathrm{c}$ and $\displaystyle \mathrm{a}+\mathrm{b}+\mathrm{c}=1$, then $\displaystyle 9\left(\mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2\right)$ is equal to $\displaystyle \_\_\_\_$.