Question

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 $\begin{vmatrix}a & 7 & 1 \\\ 2 b & 17 & 1 \\\ c & 17 & 1\end{vmatrix}+70=0$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

Answer 1

The correct answer is 495.
∣∣​A+6d2(A+1+8d)A+2+16d​71717​111​∣∣​+70=0
⇒A=−7 and d=6
∴c−a−b=20
S20​=495