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…

Let $\displaystyle \mathrm{A}_1, \mathrm{~A}_2, \mathrm{~A}_3$ be the three A.P. with the same common difference d and having their first terms as $\displaystyle \mathrm{A}, \mathrm{A}+1, \mathrm{~A}+2$, respectively. Let $\displaystyle a, b, c$ be the $\displaystyle 7^{\text {th }}, 9^{\text {th }}, 17^{\text {th }}$ terms of $\displaystyle A_1, A_2, A_3$, respectively such that $\displaystyle \left|\begin{array}{ccc}a & 7 & 1 \\ 2 b & 17 & 1 \\ c & 17 & 1\end{array}\right|+70=0$. If $\displaystyle a=29$, then the sum of first $\displaystyle 20$ terms of an AP whose first term is $\displaystyle c-a-b$ and common difference is $\displaystyle \frac{d}{12}$, is equal to $\displaystyle \_\_\_\_$.