Question

Shaunta is developing a recursive formula to represent an arithmetic sequence in which 5 is added to each term to determine each successive term. Which formula could represent her sequence?

f(n + 1) = f(n) + 5
f(n + 1) = f(n + 5)
f(n + 1) = 5f(n)
f(n + 1) = f(5n)

Answer 1

f(n + 1) = f(n) + 5

Reason: An arithmetic sequence with common difference 5 adds 5 to each term to get the next, so the recursive rule is a_{n+1} = a_n + 5. The other options either shift indices or multiply, not add.