Generate and model with recursive sequences

Question 1

A loan of $700 grows by 2% interest each month, then a payment of $300 is made. So Bₙ₊₁ = 1.02Bₙ − 300. What is the balance after 3 months? Round to 2 decimal places.

Answer 

Question 2

Which rule generates 4, 9, 19, 39, …?

• A. uₙ₊₁ = 3uₙ − 3
• B. uₙ₊₁ = 2uₙ + 1
• C. uₙ₊₁ = 2uₙ − 1
• D. uₙ₊₁ = uₙ + 5

Question 3

u₁ = 0 and uₙ₊₁ = uₙ + 4. Find u₄.

Answer 

Question 4

A loan of $1900 grows by 1.5% interest each month, then a payment of $200 is made. So Bₙ₊₁ = 1.015Bₙ − 200. What is the balance after 3 months? Round to 2 decimal places.

Answer 

Question 5

Which rule generates 4, 7, 13, 25, …?

• A. uₙ₊₁ = 3uₙ − 5
• B. uₙ₊₁ = 2uₙ − 1
• C. uₙ₊₁ = uₙ + 3
• D. uₙ₊₁ = uₙ + 2

Question 6

u₁ = 3 and uₙ₊₁ = 2uₙ − 4. Find u₄.

Answer 

Question 7

A loan of $1100 grows by 1% interest each month, then a payment of $100 is made. So Bₙ₊₁ = 1.01Bₙ − 100. What is the balance after 3 months? Round to 2 decimal places.

Answer 

Question 8

Which rule generates 3, 12, 39, 120, …?

• A. uₙ₊₁ = 3uₙ − 3
• B. uₙ₊₁ = 3uₙ + 3
• C. uₙ₊₁ = 4uₙ + 0
• D. uₙ₊₁ = uₙ + 9

Question 9

u₁ = 1 and uₙ₊₁ = 2uₙ − 3. Find u₄.

Answer 

Question 10

A loan of $800 grows by 2% interest each month, then a payment of $200 is made. So Bₙ₊₁ = 1.02Bₙ − 200. What is the balance after 3 months? Round to 2 decimal places.

Answer 

Question 11

Which rule generates 4, 7, 13, 25, …?

• A. uₙ₊₁ = 2uₙ − 1
• B. uₙ₊₁ = 2uₙ + 1
• C. uₙ₊₁ = 3uₙ − 5
• D. uₙ₊₁ = uₙ + 3

Question 12

u₁ = −3 and uₙ₊₁ = −2uₙ + 1. Find u₄.

Answer 

Question 13

A loan of $1300 grows by 1.5% interest each month, then a payment of $200 is made. So Bₙ₊₁ = 1.015Bₙ − 200. What is the balance after 3 months? Round to 2 decimal places.

Answer 

Question 14

Which rule generates 2, 3, 5, 9, …?

• A. uₙ₊₁ = uₙ + 1
• B. uₙ₊₁ = 3uₙ − 3
• C. uₙ₊₁ = 2uₙ + 1
• D. uₙ₊₁ = 2uₙ − 1

Question 15

u₁ = 2 and uₙ₊₁ = uₙ + 4. Find u₄.

Answer 

Question 16

A loan of $1800 grows by 1.5% interest each month, then a payment of $100 is made. So Bₙ₊₁ = 1.015Bₙ − 100. What is the balance after 3 months? Round to 2 decimal places.

Answer