n | f(n)
0 | 2
1 | 6
2 | 10
3 | 14

Pattern: linear because it has a constant pattern

Recursive:

f(0)=2

f(n)=f(n-1)+ 4

Explicit:

f(n)=4x+2

n | f(n)
0 | 2
1 | 4
2 | 8
3 | 16

This is exponential because it has a constant ratio.

Recursive: 

f(0)=2

f(n)=f(n-1)*2

Explicit: f(n)=(2)(2)^n

n | f(n)
0 | 1
1 | 2
2 | 5
3 | 10

This is quadratic because the 2nd difference is constant.

Recursive: 

f(0)=1

f(n)=f(n-1)+2n-1

Explicit: f(n)=n^2+1