Which of the following statements about the sequence defined by a_n = 3n + 1 is

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Question: Which of the following statements about the sequence defined by a_n = 3n + 1 is true? (2023)

Options:

Correct Answer: It is an arithmetic sequence.

Exam Year: 2023

Solution:

The sequence defined by a_n = 3n + 1 has a constant difference between consecutive terms, hence it is an arithmetic sequence.

Which of the following statements about the sequence defined by a_n = 3n + 1 is true? (2023)

Which of the following statements about the sequence defined by a_n = 3n + 1 is true? (2023)

Step 1: Understand the formula a_n = 3n + 1, where n is a positive integer (1, 2, 3, ...).
Step 2: Calculate the first few terms of the sequence by plugging in values for n:
- For n = 1: a_1 = 3(1) + 1 = 4
- For n = 2: a_2 = 3(2) + 1 = 7
- For n = 3: a_3 = 3(3) + 1 = 10
- For n = 4: a_4 = 3(4) + 1 = 13
Step 3: List the terms you calculated: 4, 7, 10, 13.
Step 4: Find the difference between consecutive terms:
- 7 - 4 = 3
- 10 - 7 = 3
- 13 - 10 = 3
Step 5: Notice that the difference between each pair of consecutive terms is the same (3).
Step 6: Conclude that since the difference is constant, the sequence is an arithmetic sequence.

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