The name 'Triangular Number' is given to any number in the series ~
If you do not spot a pattern in that list then spend a moment thinking about the difference between the first and second numbers on the list ~ and then the difference between the second and the third ~ and ~ and ~
Visualization of some triangular numbers explains almost everything you will need to know. This pattern ~ below ~ illustrates the triangular number 10.
There are fifteen red balls on a snooker table ~ 15 is the next triangular number following on from 10.