Question

Kylie starts with $145 in her piggy bank. Each month she adds $20.

Which recursive function rule models the total amount in Kylie’s piggy bank at the end of each month?


1. an=20⋅an−1 ​ and a1=145

2. an=20+an−1 ​ and a1=145

3. an=145+an−1 and a1=20

4. an=145⋅an−1 and a1=20

Answer 1

2. an=20+an−1 and a1=145

she starts with 145 so a1=145 and then adds 20 every month: an=20+an−1

Answer 2

2.
`a_(n) = a_(n-1) + 20` and
`a_(1) = 145`

Explanation:

We are given that, Kylie started with $145 in her piggy bank i.e. the initial amount in the piggy bag is $145 i.e.
`a_(1)=145`

Now, it is provided that Kylie adds $20 each month in her piggy bank i.e. at the end of each month $20 is being added to the previous amount.

Hence, the recursive function is:
`a_(n) = a_(n-1) + 20` , where the initial amount is
`a_(1) =145`.