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 .