Question

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 afterthe first weekA.f(n) = f(n-1) - 150, given f(1) = 25B.f(n) = f(n - 1) - 25, given f(1) = 150C.f(n) = f(n - 2) - 25, given f(1) = 150D.f(n) = 6f (n 1), given f(1) = 25

Answer 1

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

In this case, the recursive rule is:

`a_n=a_(n-1)-25n`
`\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}`

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

`\begin{gathered} a_1=a_(1-1)-25(1) \\ a_1=a_0-25_{} \\ a_1=150-25=125 \end{gathered}`