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?

A. f(n + 1) = f(n) + 1.5
B. f(n + 1) = f(n) + 0.75
C. f(n + 1) = f(n)
D. f(n + 1) = f(n)

Answer 1

It would be f(n+1) = f(n)+0.75

So, OPTION B IS YOUR ANSWER.........

Answer 2

Let

`f(1)=1.5\\ f(2)=2.25\\ f(3)=3\\ f(4)=3.75`

we know that

`f(2)-f(1)=2.25-1.5=0.75\\ f(2)=f(1)+0.75\\ \\ f(3)-f(2)=3-2.25=0.75\\ f(3)=f(2)+0.75\\ \\ f(4)-f(3)=3.75-3=0.75\\ f(4)=f(3)+0.75\\ \\.\\.\\.\\ f(n+1)=f(n)+0.75`

This is an arithmetic sequence, the common difference is equal to
`0.75`

therefore

the answer is the option

B. f(n + 1) = f(n) + 0.75