If \(f: \mathrm{N} \rightarrow \mathrm{Z}\) is defined by \(f\left(n\right)=\left|\begin{matrix}n & -1 & -5 \\ -2{n}^{2}…

If \(f: \mathrm{N} \rightarrow \mathrm{Z}\) is defined by \(f\left(n\right)=\left|\begin{matrix}n & -1 & -5 \\ -2{n}^{2} & 3(2k+1) & 2k+1 \\ -3{n}^{3} & 3k(2k+1) & 3k(k+2)+1\end{matrix}\right|,k\in N,\text{ and }\)\(\sum _{n=1}^{k}f\left(n\right)=98\) then \(k\) is equal to:

[JEE Main 2026, 5 Apr (Shift 2)]