Question 1: Write the formula for the nth term of an arithmetic sequence with first term 5 and common difference 3.

Answer: a_n = 5 + (n - 1) imes 3

Question 2: Calculate the 10th term of the sequence where a_1 = 2 and d = 4.

Answer: 38

Question 3: Find the 15th term of an arithmetic sequence with first term 7 and common difference -2.

Answer: -13

Question 4: In a sequence, the 5th term is 20 and the common difference is 3. Find the first term.

Answer: 5

Question 5: Plot the graph of y = 2n + 1 for n = 1 to 10.

Answer: Students will draw the points (1,3), (2,5), (3,7), ..., (10,21) and connect them.

Question 6: A sequence has a first term of 12 and a 4th term of 24. Find the common difference.

Answer: 3

Question 7: The 8th term of an arithmetic sequence is 50. The 3rd term is 35. Find the first term and the common difference.

Answer: {"d":"5","a1":"20"}

Question 8: A car travels along a straight road such that its speed increases by 2 km/h each minute. Starting from 10 km/h, what will be its speed after 15 minutes?

Answer: 40

Question 9: A sequence starts with 3, and each subsequent term increases by 5. What is the 20th term?

Answer: 98

Question 10: Explain why the formula for the nth term of an arithmetic sequence is a_n = a_1 + (n - 1)d. Provide an example with your explanation.

Answer: Students should describe the pattern of adding the common difference d repeatedly starting from a_1 to reach the nth term.

Question 11: Identify and correct the mistake in this calculation: Given a_1=4, d=3, find a_5. Student's solution: a_5 = 4 + 5×3 = 19.

Answer: The mistake is in the calculation: a_5 = 4 + (5-1)×3 = 4 + 12 = 16. The student incorrectly used 5 instead of 4 in the formula.