Find the set of values of $a$ for which $\sum\limits_{r=3}^{a}{(2r+a)}{{a}^{2}}$. [5]

Question

Find the set of values of $a$ for which $\sum\limits_{r=3}^{a}{(2r+a)}>{{a}^{2}}$. [5]

Accepted Answer

Required set$=\left\{ a\in {{\mathbb{Z}}^{+}}:a>3 \right\}$

2015 TJC MYCT Q1