Let $A _ { 1 } , A _ { 2 } , A _ { 3 }$ be the three A.P. with the same common difference $d$ and having their first terms as $A , A + 1 , A + 2$, respectively. Let $a , b , c$ be the $7 ^ { \text {th} } , 9 ^ { \text {th} } , 17 ^ { \text {th} }$ terms of $A _ { 1 } , A _ { 2 } , A _ { 3 }$, respectively such that $\left| \begin{array} { l l l } a & 7 & 1 \\ 2 b & 17 & 1 \\ c & 17 & 1 \end{array} \right| + 70 = 0$. If $a = 29$, then the sum of first 20 terms of an AP whose first term is $c - a - b$ and common difference is $\frac { d } { 12 }$, is equal to $\_\_\_\_$.
Let $A _ { 1 } , A _ { 2 } , A _ { 3 }$ be the three A.P. with the same common difference $d$ and having their first terms as $A , A + 1 , A + 2$, respectively. Let $a , b , c$ be the $7 ^ { \text {th} } , 9 ^ { \text {th} } , 17 ^ { \text {th} }$ terms of $A _ { 1 } , A _ { 2 } , A _ { 3 }$, respectively such that $\left| \begin{array} { l l l } a & 7 & 1 \\ 2 b & 17 & 1 \\ c & 17 & 1 \end{array} \right| + 70 = 0$. If $a = 29$, then the sum of first 20 terms of an AP whose first term is $c - a - b$ and common difference is $\frac { d } { 12 }$, is equal to $\_\_\_\_$.