Generate and model with recursive sequences

Question 1

u₁ = −3 and uₙ₊₁ = 3uₙ + 4. Find u₄.

Answer 

Question 2

Which rule generates 4, 10, 22, 46, …?

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

Question 3

A loan of $1400 grows by 1.5% interest each month, then a payment of $400 is made. So Bₙ₊₁ = 1.015Bₙ − 400. What is the balance after 3 months? Round to 2 decimal places.

Answer 

Question 4

u₁ = 4 and uₙ₊₁ = 2uₙ − 2. Find u₄.

Answer 

Question 5

Which rule generates 1, 1, 1, 1, …?

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

Question 6

A loan of $1100 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 

Question 7

u₁ = 6 and uₙ₊₁ = −2uₙ + 1. Find u₄.

Answer 

Question 8

Which rule generates 4, 13, 40, 121, …?

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

Question 9

A loan of $900 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 10

u₁ = −3 and uₙ₊₁ = 3uₙ + 0. Find u₄.

Answer 

Question 11

Which rule generates 4, 9, 19, 39, …?

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

Question 12

A loan of $500 grows by 2% interest each month, then a payment of $400 is made. So Bₙ₊₁ = 1.02Bₙ − 400. What is the balance after 3 months? Round to 2 decimal places.

Answer 

Question 13

u₁ = −3 and uₙ₊₁ = −2uₙ + 2. Find u₄.

Answer 

Question 14

Which rule generates 1, 5, 17, 53, …?

• A. uₙ₊₁ = 3uₙ + 2
• B. uₙ₊₁ = 4uₙ + 1
• C. uₙ₊₁ = uₙ + 3
• D. uₙ₊₁ = 3uₙ − 2

Question 15

A loan of $600 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 16

u₁ = −4 and uₙ₊₁ = −2uₙ − 4. Find u₄.

Answer