You are adding three to the last term to get to the next one.
a = - 5
d = 3
Explicit Formula
tn = a + (n - 1)*d
Example
t4 = -5 + (4 - 1)*3
t4 = -5 +3*3
t4 = -5 + 9
t4 = 4 which is exactly what you show.
Recursive formula
f(n) = f(n - 1) + 3
Example
n = 5
f(5) = f(4) + 3
f(5) = 4 + 3
f(5) = 7
