Let the sum of the first n terms of a non-constant A.P., a1, a2, a3,... be 50n + n(n-7)/2A, where A is a constant. If d is the common difference of this A.P., then the ordered pair (d, a50) is equal to?

Correct option is A (A, 50 + 46A)
Sn = 50n + n(n-7)/2A
T_n = S_n - S_{n-1} = 50n + n(n-7)/2A - [50(n-1) + (n-1)(n-8)/2A]
= 50 + A/2[n^2 - 7n - (n^2 - 9n + 8)]
= 50 + A(n - 4)
d = T_n - T_{n-1} = 50 + A(n - 4) - [50 + A(n - 5)] = A
T_50 = 50 + 46A
(d, A_50) = (A, 50 + 46A).