Question 1: Find the first four terms of a quadratic sequence if the second difference is 6 and the first term is 3.

Answer: 3, 9, 17, 27

Question 2: Calculate the second difference of the sequence: 4, 10, 18, 28.

Answer: 6

Question 3: Construct the next term in the sequence: 2, 6, 12, 20.

Answer: 30

Question 4: Identify the pattern: 5, 13, 25, 41. What is the next term?

Answer: 61

Question 5: Using the difference method, find the quadratic sequence with first term 2 and second difference 8.

Answer: 2, 8, 18, 32, 50

Question 6: The sequence 1, 4, 9, 16, ... is quadratic. Find the second difference and confirm the sequence is quadratic.

Answer: 2, sequence confirmed quadratic

Question 7: A pattern in the growth of a plant follows the sequence: 3, 6, 12, 20, 30. Use the difference method to predict the next term.

Answer: 42

Question 8: Explain why the difference method is useful for identifying quadratic sequences.

Answer: Because the second difference remains constant in quadratic sequences, making it easier to find missing terms and analyze their pattern.

Question 9: Given the sequence 7, 15, 27, 43, what is the second difference, and what does this tell you about the sequence?

Answer: 8, sequence is quadratic

Question 10: Identify the mistake in this sequence: 2, 6, 12, 18, 28. Why is it incorrect if assuming quadratic growth?

Answer: The sequence's second differences are inconsistent, indicating it is not quadratic.

Question 11: Challenge: Derive a quadratic sequence with a first term of 4 and a second difference of 10, then find its first five terms.

Answer: 4, 14, 30, 48, 68