Work out an nth term formula for the triangular numbers 1,3,6,10,15,21,...

2. Hello,
Originally Posted by suhaster
Work out an nth term formula for the triangular numbers 1,3,6,10,15,21,...

$\displaystyle \begin{array}{|c||c|c} \text{Rank }(n) & a_n & \text{Difference with the previous term} \\ \hline 1 & 1 & \emptyset \\ 2 & 3 & 2=n \\ 3 & 6 & 3=n \\ 4 & 10 & 4=n \\ 5 & 15 & 5=n \end{array}$
So, what is $\displaystyle a_{n}-a_{n-1}$ ?
3. $\displaystyle T_n = \sum\limits_{k = 1}^n k$