Mathematics - Sequence & Series Question with Solution | TestHub

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$\left|\begin{array}{lll}a& 7& 1\\ 2b& 17& 1\\ c& 17& 1\end{array}\right|+70=0$. 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 _____ .