Question 1: Find the nth term formula for the sequence: 3, 7, 11, 15, ...

Answer: a_n = 4n - 1

Question 2: Determine the nth term for the sequence: 10, 8, 6, 4, ...

Answer: a_n = -2n + 12

Question 3: What is the 10th term of the sequence: 5, 8, 11, 14, ...?

Answer: 35

Question 4: Construct the nth term formula for the sequence: 2, 5, 8, 11, ...

Answer: a_n = 3n - 1

Question 5: Find the 15th term of the sequence: 7, 10, 13, 16, ....

Answer: 46

Question 6: A sequence starts with 20 and increases by 4 each time. Write the nth term formula.

Answer: a_n = 4n + 16

Question 7: The sequence is 12, 9, 6, 3, ... Find its nth term.

Answer: a_n = -3n + 15

Question 8: Explain how to find the nth term formula for the sequence: 1, 4, 7, 10, ...

Answer: Identify the common difference (3), then use the first term to set up the formula: a_n = 3n - 2.

Question 9: Given the sequence: 50, 45, 40, 35, ... — find the nth term and determine the 20th term.

Answer: a_n = -5n + 55; a_20 = -5(20) + 55 = -100 + 55 = -45

Question 10: Identify and correct the mistake: The sequence 2, 4, 6, 8... has nth term formula a_n = 2n + 2.

Answer: Incorrect; the correct formula is a_n = 2n.

Question 11: Challenge: Write the nth term formula for the sequence where the first term is 3, and the common difference increases by 1 each time (sequence: 3, 5, 8, 12, ...).

Answer: a_n = (n^2) + 1