Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function which satisfies \(f(x+y)=f(x)+f(y) \ \forall x, y \in \mathbb…

Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function which satisfies \(f(x+y)=f(x)+f(y) \ \forall x, y \in \mathbb{R}\). If \(f(1)=2\) and \(g(n)=\sum_{k=1}^{(n-1)} f(k), n \in \mathbb{N}\) then the value of \(n\), for which \(g(n)=20\), is:

[JEE Main 2020, 2 Sep (Shift 2)]