Question

Which of the following is an A.P.?

• A. 0, 3, 0.33, 0.333, ...
• B. 1, 11, 111, ...
• C. 2, 4, 8, 16, ...
• D. 0, -4, -8, -12, ...

Hint:

To identify an A.P., check if the difference between consecutive terms is constant.

Answer 1

The Correct Option is D

Step 1: An arithmetic progression (A.P.) is a sequence where the difference between consecutive terms is constant. This difference is called the common difference. Step 2: Let's check the options for a constant difference: - For option (A): The difference is not constant.
- For option (B): The difference is not constant.
- For option (C): The difference is not constant.
- For option (D): The common difference is \( -4 \), as each term decreases by 4. Thus, the correct answer is \( 0, -4, -8, -12, \dots \).