Arecursive rule for a geometric sequence is a1=3; an=12an−1 . what is the explicit rule for this sequence?

From the recursive rule, you can tell the initial value is 3 and the common ratio is 12. The explicit rule is always
.. (n-th term) = (initial value)*(common ratio)^(n -1)

Subsituting the values you know, you have
.. an = 3*12^(n-1)