What is the third term in the arithmetic sequence that starts with 2 and has a common difference of 5?

What is the third term in the arithmetic sequence that starts with 2 and has a common difference of 5?

• A. 7
• B. 10
• C. 12
• D. 15

Answer: (C)

In an arithmetic sequence, each term is generated by adding a constant value, known as the common difference, to the previous term. In this case, the sequence starts with 2 and has a common difference of 5. To find the terms of the sequence: 1. The first term is 2. 2. The second term is found by adding the common difference to the first term: \(2 + 5 = 7\). 3. The third term is found by adding the common difference to the second term: \(7 + 5 = 12\). Thus, the third term of the sequence is 12. This confirms that the correct answer accurately reflects the process of adding the common difference to each preceding term. Understanding this pattern is essential for identifying terms in arithmetic sequences effectively.

In an arithmetic sequence, each term is generated by adding a constant value, known as the common difference, to the previous term. In this case, the sequence starts with 2 and has a common difference of 5.

To find the terms of the sequence:

1. The first term is 2.

2. The second term is found by adding the common difference to the first term:

(2 + 5 = 7).

3. The third term is found by adding the common difference to the second term:

(7 + 5 = 12).

Thus, the third term of the sequence is 12. This confirms that the correct answer accurately reflects the process of adding the common difference to each preceding term. Understanding this pattern is essential for identifying terms in arithmetic sequences effectively.