Question 1: Find the nth term of the quadratic sequence: 3, 8, 15, 24, ...

Answer: n^2 + 2n

Question 2: Determine the nth term of the sequence: 2, 6, 12, 20, ...

Answer: n^2 + n

Question 3: Calculate the 5th term of the sequence: 1, 6, 15, 28, ...

Answer: 42

Question 4: Construct a quadratic sequence where the nth term is 2n^2 + 3n + 1. Find the 4th term.

Answer: 33

Question 5: Given the sequence: 5, 14, 27, 44, ..., find the explicit formula for the nth term.

Answer: 2n^2 + 3n - 0

Question 6: A pattern of numbers is generated by the formula T(n) = n^2 + 4n + 1. Find the 10th term.

Answer: 141

Question 7: Explain why the sequence 2, 6, 12, 20, ... has the nth term n^2 + n. Show your reasoning.

Answer: Because the differences increase by 2, indicating a quadratic pattern, and fitting the terms yields n^2 + n.

Question 8: Identify and correct the mistake in the proposed nth term formula: T(n) = 2n^2 + 3n + 4 for the sequence 3, 8, 15, 24, ...

Answer: The correct formula is n^2 + 2n. The given formula does not fit the sequence.

Question 9: For the sequence: 4, 9, 16, 25, ... find the nth term and explain your method.

Answer: The sequence consists of perfect squares; nth term = n^2.

Question 10: Challenge: Derive a quadratic formula for a sequence where T(n) = 3n^2 + 2n + 5, and verify the 6th term.

Answer: T(6)=3(36)+2(6)+5=108+12+5=125

Question 11: Plot the graph of T(n) = n^2 + n for n from 1 to 10 on the grid.

Answer: Student draws on grid