Final answer:
The recursive formula for the sequence 4, -12, 36, -108, ... is given by a_n = a_(n-1) * (-3), with a_1 = 4, which most closely matches option C in the provided choices.
Step-by-step explanation:
The recursive formula for the given geometric sequence, which is 4, -12, 36, -108, ..., can be determined by recognizing the pattern that each term is multiplied by -3 to obtain the next term. The first term of the sequence is 4. To find the general recursive formula, we define it as a function of the previous term. So, the recursive formula would be an = -3 × an-1, with the first term given by a1 = 4. This is not explicitly stated in any of the options provided, but the correct structure can be observed in option C: an = an-1 × (-3), a1 = 4.