How do I find the sum of a sequence whose common difference is in Arithmetic Progression? How do I find the sum of a sequence whose common difference is in Arithmetic Progression ?
Like in the following series :-
$1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91$
And also how to find it's $n^{th}$ term ??

Empirically:
By educated guess, as the differences grows as $n$, the terms grow as $n^2$. Taking the ratios $T_n/n^2$, you see them converging to $1/2$.
Then the sequence of $2T_n-n^2$ is
$$1,2,3,4,5,6,7,\cdots$$
