Which sequence is an arithmetic progression with common difference −4?
Answer and explanation
Correct answer: 9, 5, 1, −3, …
An arithmetic progression has one constant difference between every pair of consecutive terms. For option A, 5 − 9 = −4, 1 − 5 = −4, and −3 − 1 = −4, so every step has the required common difference. Option B has differences −5, −4, and −4; option C has differences +4 throughout, so it is an AP but not with difference −4; option D has differences −4 and −5, so its difference is not constant. Therefore option A is the only sequence satisfying both conditions: it is an AP and its common difference is −4.
Frequently asked questions
What is the correct answer to this question?
9, 5, 1, −3, …
Why is this the correct answer?
An arithmetic progression has one constant difference between every pair of consecutive terms. For option A, 5 − 9 = −4, 1 − 5 = −4, and −3 − 1 = −4, so every step has the required common difference. Option B has differences −5, −4, and −4; option C has differences +4 throughout, so it is an AP but not with difference −4; option D has differences −4 and −5, so its difference is not constant. Therefore option A is the only sequence satisfying both conditions: it is an AP and its common difference is −4.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..
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