Question 1: Find the second difference for the sequence: 3, 8, 15, 24, 35.

Answer: 2

Question 2: Determine the nth term of the sequence: 2, 6, 12, 20, 30, using the Difference Method.

Answer: n^2 + n

Question 3: Construct the first three differences for the sequence: 5, 9, 15, 23, 33.

Answer: 4, 6, 8

Question 4: Identify whether the sequence 4, 9, 16, 25, 36 is quadratic using the difference method.

Answer: Yes

Question 5: Using the second difference, find the nth term for the sequence: 1, 4, 9, 16, 25.

Answer: n^2

Question 6: Explain how the Difference Method helps in identifying quadratic sequences.

Answer: The Difference Method shows that if the second differences are constant, the sequence is quadratic, allowing us to find the nth term.

Question 7: Find the third term of the sequence where the first difference is 3, second difference is 4, and the second difference is constant.

Answer: 13

Question 8: A sequence begins with 2, 6, 12. Using the Difference Method, find the next two terms.

Answer: 20, 30

Question 9: The sequence: 1, 4, 9, 16, 25 is quadratic. Find the second difference and the nth term.

Answer: 2; n^2

Question 10: Identify the common mistake: A student calculates the second difference as 5 for the sequence 2, 4, 8, 14, 22. Correct the mistake.

Answer: The second difference is 2, not 5. The differences are 2, 4, 6, 8.

Question 11: Challenge: Given the sequence 3, 10, 21, 36, find the nth term using the Difference Method.

Answer: n^2 + 2n