Final answer:
The explicit equation for the given geometric sequence is an = 534 × (0.5)(n-1). This represents the nth term of the sequence using the first term and the common ratio, which is 0.5.
Step-by-step explanation:
The given sequence is a geometric sequence where each term is half of the previous term. To find an explicit equation for this sequence, we need to identify the first term (a1) and the common ratio (r). In this case, a1 is 534 and the common ratio is ½ or 0.5 since each term is half of the one before it.
The general form of the explicit equation for a geometric sequence is an = a1 × r(n-1). Substituting our values in, we get an = 534 × (0.5)(n-1).