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) = f(n)

f(n + 1) = f(n)

Answer 1

Answer: Hello mate!

The sequence is 1.5, 2.25, 3.0, 3.75, ...

To find the common difference, let's calculate the difference between consecutive elements:

2.25 - 1.5 = 0.75

3 - 2.25 = 0.75

3.75 - 3 = 0.75

now we can see that the common difference is 0.75

then the sequence can be written as:

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

where f(1) = 1.5

then, the right option is the second one.

Answer 2

The correct option is 2.

Explanation:

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

1.5, 2.25, 3.0, 3.75, ...

It is an AP, where first term is 1.5 and common difference is

`d=a_2-a_1=2.25-1.5=0.75`

The recursive formula of an AP is

`a_n=a_(n-1)+d`

It can also be written as

`a_(n+1)=a_(n)+d`

`f(n+1)=f(n)+0.75`

Therefore the correct option is 2.