Question 1: Calculate the next term x₂ if x₁ = 3 and the iterative formula is xₙ₊₁ = 2xₙ + 1.

Answer: 7

Question 2: Given x₁ = 4 and xₙ₊₁ = xₙ² - 3, find x₂.

Answer: 13

Question 3: Construct an iterative sequence starting with x₁ = 1 and using xₙ₊₁ = xₙ + 2. Find x₄.

Answer: 5

Question 4: Plot the graph of y = 0.5x starting from x = 0 to x = 10. Use the grid to draw the points.

Answer: Students will plot the points at (0,0), (2,1), (4,2), (6,3), (8,4), (10,5).

Question 5: Identify the fixed point of the iterative function xₙ₊₁ = 3xₙ / (xₙ + 2).

Answer: 2

Question 6: If x₁ = 5 and xₙ₊₁ = xₙ - 1, what is x₃?

Answer: 3

Question 7: Solve the multi-step problem: Starting with x₁ = 2, apply xₙ₊₁ = 2xₙ + 4 for three iterations. What is x₄?

Answer: 20

Question 8: A population starts with 100 and increases each year according to xₙ₊₁ = 1.1xₙ. Calculate the population after 3 years.

Answer: 133

Question 9: Identify and correct the mistake in this iterative calculation: starting with x₁=2, x₂ = x₁ / 2 = 1, then x₃ = x₂ / 2 = 0.5.

Answer: Error: The calculation should use the formula xₙ₊₁ = 2xₙ + 1, not dividing.

Question 10: For the function xₙ₊₁ = 5 - xₙ, find the fixed point and explain its significance.

Answer: The fixed point is 5, indicating the sequence remains at 5 once reached.

Question 11: Determine the behavior of the sequence starting with x₁=0 and applying xₙ₊₁ = xₙ² - 1. Will it converge or diverge?

Answer: Diverge, as the values grow large in magnitude.

Question 12: Challenge: Find x₁ if the sequence converges to 3 using xₙ₊₁ = (xₙ + 2) / 2.

Answer: 1