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

Answer:

2. $a_{n} = a_{n-1} + 20$  and $a_{1} = 145$

Step-by-step 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 $a_{1} =145$.