Question

Jesse starts saving for his first car by opening a savings account and depositing $100. He plans to make a deposit every month to continue saving. The amount of money in Jesse's savings account can be modeled by the sequence A0=100, An=An−1+75, where n is the number of months since his initial deposit. What is the domain of the sequence An?

Answer 1

The Positive Integers

Explanation:

Imagine Math

Answer 2

Therefore the domain of the sequence is
`\{100,175,250,325,......\}`.

Explanation:

Given that, Jesse starts for his first car by opening a saving account and depositing $100.

The amount of money in Jesse's savings account can be modeled by the sequence

`A_n=A_(n-1)+75` ,
`A_0=100`

Now putting n=1

`A_1=A_(1-1)+75`

`\Rightarrow A_1=A_0+75`

`\Rightarrow A_1=100+75`

`\Rightarrow A_1=175`

Now putting n=2

`A_2=A_(2-1)+75`

`\Rightarrow A_2=A_1+75`

`\Rightarrow A_1=175+75`

`\Rightarrow A_1=250`

Now putting n=3

`A_3=A_(3-1)+75`

`\Rightarrow A_3=A_2+75`

`\Rightarrow A_3=250+75`

`\Rightarrow A_3=325`

Therefore the domain of the sequence is
`\{A_0,A_1,A_2,A_3,..........\}`

`=\{100,175,250,325,......\}`