Let \(a_1, a_2, a_3, \ldots .\). be an A.P. If \(a_7=3\), the product \(a_1 a_4\) is minimum and the sum of its first \(…

Let \(a_1, a_2, a_3, \ldots .\). be an A.P. If \(a_7=3\), the product \(a_1 a_4\) is minimum and the sum of its first \(n\) terms is zero, then \(n !-4 a_{n(n+2)}\) is equal to:

[JEE Main 2023, 31 Jan (Shift 2)]