Final answer:
A recursive function for the geometric sequence 1, 3, 9, 27, 81, ... multiplies the nth-1 term by 3 to get the nth term, starting with the base case where the first term is 1.
Step-by-step explanation:
The given sequence 1, 3, 9, 27, 81, ... is a geometric sequence where each term is obtained by multiplying the previous term by 3. To write a recursive function to compute the nth term of this sequence, we can use the relationship that each term is three times the preceding term. Here's how we can define such a function:
def recursive_sequence(n):
if n == 1:
return 1
else:
return 3 * recursive_sequence(n - 1)
This function states that if the term requested is the first term (n=1), it will return 1. If not, it will multiply the result of the nth-1 term by 3 to get the nth term. This is a simple example of a recursive function in programming.