Question 1: Write the formula for the nth term of an arithmetic sequence.

Answer: a_n = a_1 + (n - 1)d

Question 2: Find the 10th term of an arithmetic sequence where the first term is 5 and the common difference is 3.

Answer: 32

Question 3: Calculate the 15th term of an arithmetic sequence with a_1 = 2 and common difference d = 4.

Answer: 58

Question 4: A sequence has a first term of 8 and a common difference of -2. What is the 12th term?

Answer: 2

Question 5: Using the formula a_n = 3 + (n - 1)5, find the 20th term.

Answer: 93

Question 6: A sequence's 4th term is 15, and its 8th term is 27. Find the first term and the common difference.

Answer: a_1 = 7, d = 2

Question 7: Determine the value of n when the nth term of the sequence a_n = 2 + (n - 1)6 reaches 38.

Answer: 7

Question 8: Construct an arithmetic sequence with a first term of 4 and a common difference of 3. Write the formula for the nth term.

Answer: a_n = 4 + (n - 1)3

Question 9: Identify the error: The formula for the nth term is given as a_n = 2 + n + d, where d is the common difference. Explain and correct the mistake.

Answer: Incorrect because the formula should be a_n = a_1 + (n - 1)d. The error is adding n instead of (n - 1) to a_1.

Question 10: Plot the point corresponding to the 10th term in the sequence where a_1=3 and d=2 on the grid.

Answer: Plot point at (10, 3 + (10 - 1)2) = (10, 21)

Question 11: Challenge: The 5th term of a sequence is 20, and the 9th term is 32. Find the first term and the common difference. Then write the nth term formula.

Answer: a_1 = 12, d = 2, a_n = 12 + (n - 1)2