College

Leanne has a gas card that has $150 on it. She spends $25 a week on gas. Write a recursive rule that represents the amount of money she has on her gas card after the first week.

A. [tex]f(n) = f(n-1) - 150, \text{ given } f(1) = 25[/tex]
B. [tex]f(n) = f(n-1) - 25, \text{ given } f(1) = 150[/tex]
C. [tex]f(n) = f(n-2) - 25, \text{ given } f(1) = 150[/tex]
D. [tex]f(n) = 6f(n-1), \text{ given } f(1) = 25[/tex]

Answer :

Recursive rules shows the relationship between previous value and the current value.

In this case, the recursive rule is:

[tex]a_n=a_{n-1}-25n[/tex][tex]\begin{gathered} a_{n-1}=\text{ initial amount of money on the card} \\ a_n=\text{ It's the amount after n we}eks \end{gathered}[/tex]

So, for n=1 it would be the amount in the card after the first week,

[tex]\begin{gathered} a_1=a_{1-1}-25(1) \\ a_1=a_0-25_{} \\ a_1=150-25=125 \end{gathered}[/tex]

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