Let  ${\text{A}}_1,\hspace{0.17em}\hspace{0.17em}{\mathrm{A}}_2,\hspace{0.17em}\hspace{0.17em}{\mathrm{A}}_3$ be the three A.P. with the same common difference $\text{'}d\text{'}$ and having their first terms as $A, A + 1, A + 2,$ respectively. Let $a, b, c$ be the $7^{th}$, $9^{th}$,${17}^{th}$ terms of ${\text{A}}_1,\mathrm{\hspace{0.17em}\hspace{0.17em}}{\mathrm{A}}_2,\mathrm{\hspace{0.17em}\hspace{0.17em}}{\mathrm{A}}_3$  respectively such that $\left|\begin{array}{ccc}\mathrm{a}& 7& 1\\ 2\mathrm{b}& 17& 1\\ \mathrm{c}& 17& 1\end{array}\right|+70=0.$ If $a=29$, then the sum of first 20 terms of an A.P whose first term is $c – a – b$ and common difference is $\frac{d}{12}$, is equal to …..