Modeling with Sequences and Series Answers

Jill has 64 ounces of lemonade. Each day, her brother drinks 16 ounces. Then at the end of each day Jill adds 25% of the remaining total back into the lemonade container. Which recursive formula models the number of ounces of lemonade in the container, , at the end of the nth day?

The total number of miles Jeremy walked on a hike can be represented by using the formula . If and n represents the total number of hours walked, what is the total distance Jeremy walked at the end of each of the first three hours?

Paige borrows $700 from her parents for a new computer. She repays $100 the first month, and then begins to repay her parents $75 per month. Which recursive formula models the total amount of money still owed, , at the end of the nth month?

Johann borrows money from his parents to purchase a bike. He makes weekly payments to his parents to repay the money borrowed. The total amount of money repaid at the end of week n can be represented using the recursive formula . At the end of the fourth week, Johann had repaid his parents a total of $55. What is the total amount Johann had repaid his parents at the end of the first week?

What are the first four terms of the sequence modeled by the recursive formula , when ?

Each year, a daylily farm sells a portion of their daylilies and allows a portion to grow and divide. The recursive formula represents the number of daylilies, a, on the farm after n years. After the fifth year, the farmers estimate they have 2,225 daylilies. How many daylilies were on the farm after the first year?

What are the first three terms of the sequence defined by the recursive function , when and ?

In an arithmetic sequence, and . Which recursive formula defines the sequence?

Which formula can be used to describe the sequence below?

The amount of money in Nadia’s savings account at the end of n years is represented by the recursive formula . If , what is the balance in Nadia’s account at the end of each of the first two years?

What are the first three terms of the sequence modeled by the recursive function , when ?

What are the first four terms of the sequence defined recursively below?

What are the first two terms of the sequence defined recursively by the formula , when ?

Which formula can be used to describe the sequence below?–8, –5, –2, 1, 4, ...