What is the common difference of the arithmetic progression 0, −4, −8, −12, …?
Answer and explanation
Correct answer: −4
The governing concept is the common difference of an arithmetic progression. It is the fixed number added to one term to obtain the next term, so it is calculated as later term minus preceding term. Using the first two terms, d = (−4) − 0 = −4. The result can be checked with the next pairs: (−8) − (−4) = −4 and (−12) − (−8) = −4. Since the same value occurs each time, the sequence is an arithmetic progression with common difference −4. The negative sign is essential because the terms decrease by four units. Option B, 4, would indicate an increasing sequence, while option D is only one term and option A is not the actual change. Therefore option C is correct.
Frequently asked questions
What is the correct answer to this question?
−4
Why is this the correct answer?
The governing concept is the common difference of an arithmetic progression. It is the fixed number added to one term to obtain the next term, so it is calculated as later term minus preceding term. Using the first two terms, d = (−4) − 0 = −4. The result can be checked with the next pairs: (−8) − (−4) = −4 and (−12) − (−8) = −4. Since the same value occurs each time, the sequence is an arithmetic progression with common difference −4. The negative sign is essential because the terms decrease by four units. Option B, 4, would indicate an increasing sequence, while option D is only one term and option A is not the actual change. Therefore option C is correct.
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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