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Writing and Using Explicit Rules for Arithmetic Sequences

Exercise 1.7 - Solution

Let be the sequence representing the amount of money left on Elishia's card. At the beginning the cafeteria card's value is This means that our first term, is After the first purchase on Monday its value is and after the next day its value is As we can see the common difference is equal to

Finding our formula

We will use the generic form of an explicit formula of an arithmetic sequence. In the above formula, is the initial value and is the common difference. We will get our equation by substituting and

Finding the value of the card

Each lunch decreases the value of the card by Therefore, to find the amount of money left on the card after buying lunches, we should subtract from the initial value
After buying lunches, the card's value will be