Question

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

Answer 1

In this question, it is given that

Leanne has a gas card that has $150 on it. She spends $25 a week on gas.

And we have to Write a recursive rule that represents the amount of money she has on her gas card after the first week .

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

And here, the recursive rule is

`a_(n) = a_(n-1)-25n`

Where a(n-1) is the initial amount which is $150 . And a(n) is the amount after n week .

So for n=1, that is amount in the card after 1 week, we will get

`a_(1) = a_(1-1) -25(1) \\ a_(1) = a_(0) -25 \\ a_(1) = 150 -25 \\ a_(1) = $125`

And that's the amount remaining in the card after 1 week .