Final answer:
The recursive formula for the sequence calculator depends on the pattern in the sequence. Option a) yields the Fibonacci sequence, option b) yields a geometric sequence, and option d) yields an arithmetic sequence.
Step-by-step explanation:
The recursive formula for the sequence calculator can be found by analyzing the pattern in the sequence. Let's go through each option to determine the correct recursive formula:
a) Sn = Sn-1 + Sn-2
This formula suggests that each term in the sequence is the sum of the two previous terms. This is known as the Fibonacci sequence, where each term is the sum of the two preceding terms.
b) Sn = 2 * Sn-1
This formula states that each term in the sequence is double the previous term. This forms a geometric sequence, where each term is obtained by multiplying the previous term by a constant factor.
c) Sn = Sn-1 - Sn-2
This formula suggests that each term in the sequence is the difference between the two previous terms. This does not correspond to any common sequence.
d) Sn = 3 * Sn-1 + 2
This formula states that each term in the sequence is three times the previous term plus two. This forms an arithmetic sequence with a common difference of three.
Therefore, the correct recursive formulas for the sequence calculator are:
a) Sn = Sn-1 + Sn-2 (Fibonacci sequence)
b) Sn = 2 * Sn-1 (Geometric sequence)
d) Sn = 3 * Sn-1 + 2 (Arithmetic sequence)