Final answer:
The correct recursive formula for an arithmetic sequence where 5 is added to each term is f(n + 1) = f(n) + 5, representing the next term addition.
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. For Shaunta's sequence, where each term is determined by adding 5 to the previous term, the formula should represent how the next term is related to the current term in the sequence.
Let's analyze the given options:
f(n+1)=f(n)+5: This formula aligns with the description of the sequence. It indicates that to get the next term (f(n+1)), one needs to add 5 to the current term (f(n)). This formula correctly represents an arithmetic sequence where 5 is added to each term to determine the successive term.
f(n+1)=f(n+5): This formula suggests that the next term (f(n+1)) is equal to the term that is five steps ahead (f(n+5)). It doesn't align with the description of adding 5 to each term in an arithmetic sequence.
f(n+1)=5f(n): This formula indicates that the next term (f(n+1)) is equal to 5 times the current term (f(n)). It represents a geometric sequence where each term is multiplied by a constant (5 in this case), not an arithmetic sequence where a constant is added to each term.
f(n+1)=f(5n): This formula implies that the next term (f(n+1)) is determined by the term at 5n. It doesn't represent an arithmetic sequence where the next term is obtained by adding a constant to the current term.
Among the given options, the formula that represents Shaunta's arithmetic sequence, where 5 is added to each term to determine the successive term, is option 1: f(n+1)=f(n)+5. This formula correctly defines the recursive relationship for the arithmetic sequence she is developing.