What is the connection between the square numbers and triangular numbers

Question

in arrays as shown below with a line drawn to show the array as 3/6?
...
...
...
and
....
....
....
....
array shows 6/10?

Answer 1

if n is a natural number
then
n^2 generates the square numbers
(n^2 + n)/2 generates the triangular numbers

Does that help?

Answer 2

810