What is a recursive rule?

It is a term for sequences in which a finite number of terms are defined explicitly and then all subsequent terms are defined by the preceding terms.

The best known example is probably the Fibonacci sequence in which the first two terms are defined explicitly and after that the definition is recursive:

x1 = 1

x2 = 1

xn = xn-1 + xn-2 for n = 3, 4, ...