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

Answer: n^2 + 2n + 0

Question 2: Find the formula for the nth term of the sequence: 2, 6, 12, 20, ...

Answer: n^2 + n

Question 3: Construct the quadratic sequence with nth term: 2n^2 + 3n + 1. What is the 10th term?

Answer: 10*(2*10)+3*10+1=200+30+1=231

Question 4: Identify the error in the nth term formula: For the sequence 1, 4, 9, 16, ..., the nth term is incorrectly given as n^2 + 1.

Answer: The correct nth term is n^2, not n^2 + 1.

Question 5: Given the sequence 5, 14, 27, 44, ..., find the nth term and determine the 15th term.

Answer: nth term: 2n^2 + 3n + 0; 15th term: 2*15^2 + 3*15=2*225+45=495

Question 6: Using the sequence where the 1st term is 4 and the common second difference is 2, find the nth term.

Answer: nth term: n^2 + 3n + 0

Question 7: A sequence is defined by the nth term: 3n^2 + 2n - 5. Find the 12th term.

Answer: 3*12^2 + 2*12 - 5=432+24-5=451

Question 8: Construct the sequence where the 1st term is 1 and the nth term is 2n^2 - n. What is the 20th term?

Answer: 2*20^2 - 20=2*400-20=800-20=780

Question 9: Identify the pattern in the sequence: 7, 15, 27, 43, ... and find the nth term.

Answer: nth term: 2n^2 - n + 6

Question 10: Explain and correct the mistake: The sequence 2, 6, 12, 20 is said to have nth term n^2 + n + 1.

Answer: The correct nth term is n^2 + n; the given formula overestimates the sequence values.

Question 11: A sequence models the number of handshakes in a group of n people: 0, 1, 3, 6, 10, ... Find the nth term and the 25th handshake count.

Answer: nth term: n(n-1)/2; 25th: 25*24/2=300

Question 12: Create a quadratic sequence with the 1st term 5 and second difference 4. Find the 8th term.

Answer: nth term: 2n^2 - 3n + 6; 8th term: 2*8^2 - 3*8 + 6=128-24+6=110