Final answer:
The explicit formula for the given sequence 2, 8, 32, 128, ... is a = 2^-1(4^n-1).
Step-by-step explanation:
The given sequence 2, 8, 32, 128, ... is an example of a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio. In this case, the common ratio is 4, since each term is 4 times greater than the previous term.
To find the explicit formula for this geometric sequence, we can start with the first term, which is 2. Let n represent the position of a term in the sequence. The formula for the nth term of a geometric sequence is given by:
an = a1 * r^(n-1)
Substituting the values, we have:
an = 2 * 4^(n-1)
Therefore, the correct answer is (D) a = 2^-1(4^n-1).