TMUA 2017 Paper 1 Question 17

The two functions $F(n)$ and $G(n)$ are defined as follows for positive integers $n$: $$F(n)=\frac{1}{n}{\int }_0^n(n-x)dx,G(n)=\sum _{r=1}^{n}F(r).$$ What is the smallest positive integer $n$ such that $G(n)>150$?