The famous mathematician Gauss is said to have found a formula for that exact problem when he was in primary school. And as mentioned by @Henry in the comments it is:
Source: Wikipedia (DE), Wikipedia (EN)
As work is done for every entry, i.e., O(1) is required for each “item”. Hence, the problem is in O(n^2).
Visualisation (also Wikipedia) can be seen as a half filled square:
