Solving Recursive Formulas in Arithmetic Sequences

A gardener plants a row of flowers. The first flower is planted 2 feet from the start of the row, and each subsequent flower is planted 3 feet apart. What is the recursive formula for the distance of the nth flower from the start?

• d(n) = 3n for n >= 1

• d(n) = 2 + 4(n - 1) for n >= 1

• d(n) = 2 + 2(n - 1) for n >= 1

• d(n) = 2 + 3(n - 1) for n >= 1

In a library, the number of books on a shelf increases by 5 each month. If there are 20 books on the shelf at the start, what is the recursive formula for the number of books after n months?

• a(n) = a(n-1) - 5, a(0) = 20

• a(n) = 5n + 20

• a(n) = a(n-1) + 10, a(0) = 15

• a(n) = a(n-1) + 5, a(0) = 20

A staircase has steps that rise 4 inches higher with each step. If the first step is 6 inches off the ground, what is the recursive formula for the height of the nth step?

• h(n) = 10 + 4n for n >= 1

• h(n) = 6 + 2(n - 1) for n >= 1

• h(n) = 6 + 4(n - 1) for n >= 1

• h(n) = 4n + 2 for n >= 1

A car travels 10 miles in the first hour and increases its speed by 2 miles each hour. What is the recursive formula for the distance traveled after n hours?

• D(n) = D(n-1) + (10 + 2(n-1)), D(1) = 10

• D(n) = D(n-1) + 10, D(1) = 10

• D(n) = D(n-1) + 2n, D(1) = 10

• D(n) = D(n-1) + 12, D(1) = 10

A savings account starts with $100 and earns $15 each month. What is the recursive formula for the amount in the account after n months?

• A(n) = 100 + 15n, A(0) = 100

• A(n) = A(n-1) - 15, A(0) = 100

• A(n) = A(n-1) + 15, A(0) = 100

• A(n) = A(n-1) + 10, A(0) = 100

A concert hall has 50 seats in the first row, and each subsequent row has 8 more seats than the previous one. What is the recursive formula for the number of seats in the nth row?

• S(n) = S(n-1) + 8, S(1) = 40

• S(n) = S(n-1) + 10, S(1) = 50

• S(n) = S(n-1) + 5, S(1) = 50

• S(n) = S(n-1) + 8, S(1) = 50

A factory produces 200 toys in the first week and increases production by 50 toys each week. What is the recursive formula for the number of toys produced after n weeks?

• T(n) = T(n-1) + 30, T(1) = 200

• T(n) = T(n-1) + 50, T(1) = 200

• T(n) = T(n-1) + 50, T(1) = 150

• T(n) = T(n-1) + 100, T(1) = 200

A runner completes 3 laps in the first week and increases the number of laps by 2 each week. What is the recursive formula for the number of laps completed after n weeks?

• L(n) = L(n-1) + 2, L(1) = 3

• L(n) = L(n-1) + 1, L(1) = 3

• L(n) = L(n-1) + 2, L(1) = 5

• L(n) = L(n-1) + 3, L(1) = 1

A book series has 4 books in the first installment, and each new installment adds 3 more books. What is the recursive formula for the total number of books in the nth installment?

• T(n) = 4n for n >= 1

• T(n) = 4 + 2(n - 1) for n >= 1

• T(n) = 4 + 3(n - 1) for n >= 1

• T(n) = 7 + 3n for n >= 1

A tree grows 5 inches in the first year and continues to grow 3 inches more each subsequent year. What is the recursive formula for the height of the tree after n years?

• H(n) = H(n-1) + 3, H(1) = 10

• H(n) = H(n-1) + 3, H(1) = 5

• H(n) = H(n-1) + 5, H(1) = 5

• H(n) = H(n-1) + 2, H(1) = 5