Let $A(n)$ be the representing the amount of money left on Elishia's card. At the beginning the cafeteria card's value is $$50.$ This means that our first term, $A(1),$ is $50.$ After the first purchase on Monday its value is $$46.75,$ and after the next day its value is $$43.50.$ $50→−3.2546.75→−3.2543.5→−3.25… $
As we can see the common difference $d$ is equal to $-3.25.$

### Finding our formula

We will use the generic form of an of an arithmetic sequence.

$A(n)=A(1)+(n−1)d $
In the above formula,

$A(1)$ is the initial value and

$d$ is the common difference. We will get our equation by substituting

$A(1)=50$ and

$d=-3.25.$
$A(n)=A(1)+(n−1)d$

$A(n)=50+(n−1)(-3.25)$

$A(n)=50+(-3.25)(n−1)$

$A(n)=50−3.25(n−1)$

### Finding the value of the card

Each lunch decreases the value of the card by

$$3.25.$ Therefore, to find the amount of money left on the card after buying

$12$ lunches, we should subtract

$12⋅3.25$ from the initial value

$50.$
After buying

$12$ lunches, the card's value will be

$$11.$