Answer: The recursive formula for the sequence 2, -6, 18, -54 is given by the following:
a(n) = (-3) * a(n-1)
where a(n) is the nth term of the sequence and a(n-1) is the previous term in the sequence.
This means that each term in the sequence is equal to -3 times the previous term, with the first term being 2. For example, the third term of the sequence (a(3)) would be equal to (-3) * a(2), which is (-3) * (-6) = 18. The fourth term of the sequence (a(4)) would be equal to (-3) * a(3), which is (-3) * 18 = -54. And so on.
This recursive formula can be used to calculate the nth term of the sequence for any value of n.