What is the difference between explicit and recursive forms of sequences?

"In mathematics, a sequence is an ordered list of objects (or events)." 

An explicit sequence would be one which you have a formula to know every term of the sequence, for example: 

S(n)=2n, the list of all even numbers. 

So, if you wonder which even number is the 5th on the list, you just apply the formula and find: 

S(5)=2*5=10 that 10 is the 5th on the list. 

A recursive sequence is one in which every member of the list is defined by the preceding ones, for example: 

S(1)=2 
S(2)=S(1)+2=2+2=4 

S(n)=S(n-1)+2 

This one is also the ist of all even numbers, but if you want to know which one is the 5th number on the list, you would have to know which one is the fourth and then add 2 to it: 

S(5)=S(4)+2