Triangular numbers, rectangular numbers, etc.?

Question

Can someone please tell me the algebraic rule for finding:

Triangular numbers
Rectangular numbers
Pentagonal numbers
Hexagonal numbers

Thank you, but I meant a rule, like (N-1)/2 or something. You just listed the numbers

Answer 1

Triangular numbers:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91...
a(n) = ½(n² + n)

Square numbers:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169...
a(n) = n²

Pentagonal numbers:
1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247...
a(n) = ½(3n² - n)

Hexagonal numbers:
1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325...
a(n) = 2n² - n

Answer 2

Triangular numbers are the following

1
1+2
1+2+3
1+2+3+4

Or... 1,3,6,10,...

I've never heard of the others.