Question

Zina spends 1.5 hours setting up her sewing machine and making one hat. The total amount of time spent making hats can be represented by the sequence below.

1.5, 2.25, 3.0, 3.75, ...
Which recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously?

f(n + 1) = f(n) + 1.5
f(n + 1) = f(n) + 0.75
f(n + 1) = one-halff(n)
f(n + 1) = three-halvesf(n)

Answer 1

Answer: f(n + 1) = f(n) + 0.75.

Explanation: The sequence increases by 0.75 each term (1.5 → 2.25 → 3.0 → 3.75), so each additional hat adds 0.75 hours. With f(1)=1.5, the recurrence is f(n+1)=f(n)+0.75.