Help with a Pascal's Triangle formula

In Pascal's Triangle, you can find counting numbers, triangular numbers, polygonal numbers, etc.
I have a formula that can be used to find triangular numbers: n(n + 1)/2

It is actually equal to T(n) = 1 + 2 + 3 + ... + n.
Can someone please tell me what kind of formula this is? (Recursive, General?)
And can you also please tell me how you got it? (Like finite differences if it was a recursive formula)

Thanks!

T(n) = 1 + 2 + 3 + ... + n is not recursive because the equation would have to depend on an initial condition or another formula. Yours can be written recursively as:
T(1) = 1
T(n+1) = T(n) + 1

You can prove that n(n+1)/2 = 1 + 2 + 3 + ... + n by mathematical induction.