There are two common ways to define a sequence — you can give a formula in terms of n (the explicit formula), or you can give the first term and a "rule for generating the next term." The latter is called a recursive definition. Change the first term and the rule with the sliders and see how the terms are generated one after another.
Recursive definition vs. explicit formula: A formula such as "a_n = 2 + 3(n-1)" is an explicit formula because you can substitute n and get a term directly. By contrast, when you are given only a starting value and a rule such as "a₁=2, a(n+1)=a_n+3," you must calculate a₁→a₂→a₃→a₄→a₅ one by one to find a₅ — that is a recursive definition.
The Fibonacci sequence (1,1,2,3,5,8,…) is naturally expressed recursively — a(n+1) = a_n + a(n-1), meaning "the next term is the sum of the two preceding terms." Sequences like this are often difficult to express with a simple explicit formula.