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

Answer: n^2 + 2n

Question 2: Calculate the 10th term of the sequence: 2, 7, 14, 23, ...

Answer: n^2 + n + 1

Question 3: Construct the algebraic expression for the nth term of the sequence: 5, 12, 21, 32, ...

Answer: n^2 + 4n + 0

Question 4: A sequence starts with 1, 6, 15, 28, ... What is the nth term?

Answer: n^2 + 2n

Question 5: Identify the mistake in deriving the nth term: for the sequence 4, 9, 16, 25, ... they said the nth term is n^2 + 2.

Answer: The correct nth term is n^2 + 2n, not n^2 + 2.

Question 6: Find the 15th term of the sequence: 0, 3, 8, 15, ...

Answer: n^2 - 1

Question 7: The sequence 1, 4, 9, 16, ... has a consistent pattern. Write the nth term.

Answer: n^2

Question 8: A sequence is defined as 2, 7, 14, 23, ... Find a formula for the nth term.

Answer: n^2 + n + 1

Question 9: A student claims the nth term of 6, 11, 18, 27, ... is 2n^2 + 2. Is this correct? Explain.

Answer: No, the correct nth term is n^2 + 5n + 0.

Question 10: Determine the 8th term of the sequence: 1, 4, 9, 16, ...

Answer: 64

Question 11: Challenge: Derive the nth term for the sequence: 1, 6, 15, 28, 45, ... and find the 20th term.

Answer: n^2 + 3n - 1; 400