Final answer:
The explicit rule for the geometric sequence 15, 3, 3/5, 3/25,... is an = 15 × (1/5)n-1, where an is the nth term, 15 is the first term, and 1/5 is the common ratio.
Step-by-step explanation:
The student is asking to enter the explicit rule for a geometric sequence. Given the sequence 15, 3, 3/5, 3/25,..., we can see that each term is being divided by 5 to get the next term. This pattern shows that the sequence is a geometric sequence with a common ratio (r) of 1/5.
The explicit formula for finding the nth term of a geometric sequence is an = a1 × rn-1, where a1 is the first term and r is the common ratio. In this case, the first term a1 is 15, and the common ratio r is 1/5. Plugging these values into the formula gives us the explicit rule for the nth term: an = 15 × (1/5)n-1.