If $a + b + c = 1$ and $a < b < c , a , b , c \in R$ and $a ^ { \mathbf { 2 } } , 2 b ^ { \mathbf { 2 } } , c ^ { \mathbf { 2 } }$ are in G.P. and $a , b , c$ are in A.P. then find the value of $9 \left( a ^ { 2 } + b ^ { 2 } + c ^ { 2 } \right) =$ ?