Polygonal numbers

Use the yellow slider to explore a sequence of triangular numbers T(n) and square numbers S(n). How does T(n) depends on T(n-1) and n? What is the value of T(100)? How does S(n) depends on S(n-1) and n? What is the value of S(100)? The applet will show you the first three hexagonal numbers H(1), H(2) and H(3). Can you write an expression for H(n)? Why do all polygonal numbers seem to increase quadratically?