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

Answer: n^2 + 2n + 0

Question 2: Determine the nth term for the sequence: 2, 7, 14, 23, ...

Answer: n^2 + n + 0

Question 3: A sequence has the terms: 1, 6, 15, 28, ... Find its nth term.

Answer: n^2 + 2n - 2

Question 4: Calculate the 10th term of the sequence: 4, 13, 24, 37, ...

Answer: n^2 + 3n + 0

Question 5: Construct the quadratic sequence with nth term 2n^2 + 3n + 1. What are its first four terms?

Answer: [3, 8, 15, 24]

Question 6: If the nth term of a sequence is n^2 + 4n, what is the 15th term?

Answer: 225

Question 7: Find the nth term of a sequence where the 1st term is 5, the 2nd term is 12, the 3rd term is 21, and the 4th term is 32.

Answer: n^2 + 4n + 0

Question 8: A sequence has the terms 2, 7, 14, 23, 34. Find its nth term.

Answer: n^2 + 3n + 0

Question 9: A sequence's nth term is 3n^2 - n + 2. What is the 20th term?

Answer: 1182

Question 10: Identify the mistake in this nth term: the sequence 1, 4, 9, 16, ... with nth term n^2 + 1.

Answer: The nth term should be n^2, not n^2 + 1, as the sequence is perfect squares.

Question 11: Using the sequence 5, 16, 29, 44, find the nth term and predict the 25th term.

Answer: n^2 + 4n + 1