The triangular numbers are the following:

$\displaystyle {T}_{{1}}={1},{T}_{{2}}={3},{T}_{{3}}={6},{T}_{{4}}={10},\ldots$

They are called triangular numbers because you can think of the number as a series of dots which can be arranged into a triangle as shown below:



The formula for the nth triangular number is $\displaystyle {T}_{{n}}=\frac{{{n}{\left({n}+{1}\right)}}}{{2}}$. For example, the fourth triangular number is 10, so $\displaystyle {T}_{{4}}={10}$.

3081 is a triangular number. Which one is it?


For example, if 3081 happened to be the 4th triangular number (which of course it's not), your answer would be 4.