How did we derive this general term for the series? We have this series of numbers:
$1, 3, 6, 10, 15$
The general term can be described wit: $\frac{r(r + 1)}{2}$
Apparently the following series:
$1, 4, 10, 20, 35$
Can be described with $\frac{r(r + 1)(r + 2)}{6}$ based on the first series.
But I am not clear how this is derived. Can someone please explain?

Note: That from the given series you are not able to derive a unique expression for the general term. There are infinitly many solutions. There are some which are more obvious (see JMoravitz), but there is no mathematical definition for more obvious as far as I know.
E.G. a polynomial of 6th degree can fit all points, polynomial of 7th degree ...., all polynomial of higher degree than 6 can have an appropriate choice of coefficients so that all the given points lie on the polynomial.
