Final answer:
The explicit rule for the nth term of the geometric sequence is an = 5 * 4^(n-1), which states that to find any term in the sequence, multiply the first term (5) by 4 raised to the power of one less than the term number.
Step-by-step explanation:
The student is asking for the explicit rule for the nth term of the geometric sequence 5, 20, 80, 320, 1280, .... To determine the correct formula, we first note that each term is obtained by multiplying the previous term by 4. This means we're dealing with a geometric sequence where the first term (a1) is 5 and the common ratio (r) is 4.
The general formula for the nth term of a geometric sequence is an = a1 * r^(n-1). Substituting our known values gives us an = 5 * 4^(n-1). Thus, the correct explicit rule for the nth term of given geometric sequence is an = 5 * 4^(n-1). Given the provided options, none of them matches the correct formula exactly; however, if we assume the student provided options are incorrect, the closest resembling correct formula is an = 5(4n-1) with a typo, where the multiplication sign should be an exponent sign.