Recursive Formulas in Arithmetic Sequences for Grade 8

A gardener plants a row of 5 trees. Each tree is planted 3 feet apart. Write a recursive formula to represent the distance of the nth tree from the first tree.

• d(n) = 3(n+1) for n >= 1

• d(n) = 3(n-1) for n >= 1

• d(n) = 3n for n >= 1

• d(n) = 3(n-2) for n >= 1

A student saves $10 in the first week and increases her savings by $5 each week. What is the recursive formula for her savings after n weeks?

• S(n) = S(n-1) - 5, S(1) = 10

• S(n) = S(n-1) + 10, S(1) = 5

• S(n) = S(n-1) + 5, S(1) = 10

• S(n) = 10 + 5n, S(1) = 10

A book series has its first book released in 2010, and a new book is released every 2 years. Write a recursive formula for the year of the nth book release.

• year(n) = 2012 + 2n

• year(n) = 2010 + n

• year(n) = 2010 + 2(n - 1)

• year(n) = 2010 + 3(n - 1)

A staircase has 4 steps, and each step is 6 inches high. Write a recursive formula to find the height of the nth step from the ground.

• height(n) = 12n

• height(n) = 4n

• height(n) = 6n

• height(n) = 6n + 2

A factory produces 100 toys in the first week and increases production by 20 toys each week. What is the recursive formula for the number of toys produced in the nth week?

• T(n) = T(n-1) + 20, T(1) = 100

• T(n) = T(n-1) + 20, T(1) = 120

• T(n) = T(n-1) + 10, T(1) = 100

• T(n) = T(n-1) + 30, T(1) = 80

A concert starts with 50 attendees and gains 10 more attendees each hour. Write a recursive formula for the number of attendees after n hours.

• A(n) = 50 - 10n

• A(n) = 50 + 10n

• A(n) = 50 + n

• A(n) = 10n

A car travels 60 miles in the first hour and increases its speed by 15 miles each hour. Write a recursive formula for the distance traveled after n hours.

• D(n) = 60 + 15n

• D(n) = 60n + 15

• D(n) = 60 + 15n^2

• D(n) = 60 + 15 * (n - 1) * n / 2

A library adds 30 new books each month starting with 150 books. What is the recursive formula for the total number of books after n months?

• T(n) = T(n-1) + 20, T(0) = 150

• T(n) = T(n-1) + 30, T(0) = 200

• T(n) = T(n-1) + 30, T(0) = 150

• T(n) = T(n-1) + 30, T(0) = 100

A fitness program starts with 5 push-ups on the first day and increases by 3 push-ups each day. Write a recursive formula for the number of push-ups on the nth day.

• P(n) = 5 + 3(n - 1) for n >= 1

• P(n) = 3n + 2 for n >= 1

• P(n) = 5n for n >= 1

• P(n) = 5 + 2(n - 1) for n >= 1

A savings account starts with $200 and earns $25 each month. Write a recursive formula to represent the total amount in the account after n months.

• A(n) = 200 + 25n

• A(n) = 25n

• A(n) = 200 + 50n

• A(n) = 200 - 25n