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 7 text th , 9 text th , 17 text th terms of A1, A2, A3, respectively such that |a 7 1 2 b 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

Question

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 7 text th , 9 text th , 17 text th terms of A1, A2, A3, respectively such that |a 7 1 2 b 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 (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

| A +6 d 7 1 2( A +1+8 d ) 17 1 A +2+16 d 17 1|+70=0 ⇒ A =-7 text and d =6 ∴ c - a - b =20 S 20=495

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

$∣ ∣ A + 6 d 2 (A + 1 + 8 d) A + 2 + 16 d 71717111 ∣ ∣ + 70 = 0$
$\Rightarrow A = - 7 and d = 6$
$∴ c - a - b = 20$
$S_{20} = 495$