If $f\left(x\right)$ is a function satisfying $f\left(x+y\right)=f\left(x\right)f\left(y\right)$ $\forall x, y\in N$ such that $f\left(1\right)=3$ and $\sum _{x=1}^{n}f\left(x\right)=120$. Then, the value of $n$ is