Question 1: What is the next number in the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, ?

Answer: 13

Question 2: Identify the pattern in the sequence: 2, 4, 8, 16, 32, ?

Answer: 64

Question 3: Construct the next three terms of the sequence: 1, 3, 6, 10, 15, ?

Answer: 21, 28, 36

Question 4: A sequence starts with 5, then 10, then 20. Which of the following correctly describes the pattern?

Answer: It doubles each time

Question 5: Identify the error in this sequence: 1, 3, 6, 11, 18, ?

Answer: The pattern is adding increasing numbers (+2, +3, +5, +7), so next should be 26

Question 6: Explain why the sequence 2, 4, 8, 16, 32, 64 is a geometric sequence. What is the common ratio?

Answer: Each term is multiplied by 2, so the common ratio is 2

Question 7: Plot the first five terms of the sequence 3, 6, 12, 24, 48 on the grid.

Answer: Students draw points at 3, 6, 12, 24, 48

Question 8: Construct a triangle on the grid with side lengths following the pattern: 3, 5, 8, 13. Are these lengths forming a Fibonacci pattern? Why or why not?

Answer: No, because the pattern is not consistent with Fibonacci addition (where each term is the sum of the two previous).

Question 9: Find the next number in the sequence: 1, 4, 9, 16, 25, ?

Answer: 36

Question 10: Identify the error in this pattern and correct it: 2, 4, 8, 15, 30

Answer: The pattern doubles, so 15 should be 16; correct sequence: 2, 4, 8, 16, 32

Question 11: Challenge: Derive a general formula for the sequence: 1, 3, 5, 7, 9, ?

Answer: An explicit formula is an = 2n - 1