To determine the total amount of time Zina spends making hats based on the previous total time, we need to consider the pattern in the sequence given: 1.5, 2.25, 3.0, 3.75, ....
Let's analyze the sequence step by step:
- The first term is 1.5 hours (for making the first hat).
- The second term is 2.25 hours.
- The third term is 3.0 hours.
- The fourth term is 3.75 hours.
Observing the differences between consecutive terms:
- 2.25 - 1.5 = 0.75
- 3.0 - 2.25 = 0.75
- 3.75 - 3.0 = 0.75
The difference between each term and the previous term is consistently 0.75 hours.
Thus, the recursive formula adds 0.75 to the previous term to get the next term. Thus, the appropriate recursive formula is:
\[ f(n + 1) = f(n) + 0.75 \]
So, the correct answer is:
\[ f(n + 1) = f(n) + 0.75 \]
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)
1 answer