A recursive formula is a formula that describes a sequence #a_0, a_1, a_2, ...# by giving a rule to compute #a_i# in terms of its predecessor(s), instead of giving an immediate representation for the #i#-th term.
In this sequence, we can see that each term is three more than its predecessor, so the formula would be
#a_1 = 3#
#a_n = a_{n-1}+3#
Note that every recursive formula must have a condition to terminate the recursion, otherwise you'd be stuck in a loop: #a_n# is three more than #a_{n-1}#, which is three more than #a_{n-2}#, and you would go all the way back to infinity. Stating that #a_1=3# saves us from this infinite descend. Here's an example.
Suppose we want to compute #a_4#. We know that:
#color(red)(a_4) = color(green)(a_3)+3#
#color(green)(a_3) = a_2+3#
#a_2 = color(blue)(a_1)+3#
But now we break the recursion, because we know that #a_1=3#. So we can start working upwards:
#a_2 = color(blue)(a_1)+3 = color(blue)(3)+3 = 6#
#color(green)(a_3) = a_2+3 = 6+3 = 9#
#color(red)(a_4) = color(green)(a_3)+3 = 9 + 3 = 12#
