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

Answer:

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

Step-by-step 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 $\{A_0,A_1,A_2,A_3,..........\}$

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