Arithmetic Progressions and Determinant

Let A1,A2,A3 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 7‌th ‌,9‌th ‌,17‌th ‌ terms of A1,A2,A3, respectively such that |

a	7	1
2b	17	1
c	17	1

|+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 ‌

d

12

, is equal to ________.