What is the common difference of (15,12,9,6,\ldots)?
Answer and explanation
Correct answer: -3
The common difference of an arithmetic progression is the difference between two consecutive terms: second term − first term. Here, \(d=12-15=-3\), and the same value is obtained from \(9-12=-3\) and \(6-9=-3\). Therefore, option B, \(-3\), is correct. Since the progression is decreasing, its common difference is negative; writing only its magnitude, \(3\), would be incorrect. Exam tip: calculate \(a_2-a_1\) or subtract any term from the term immediately following it.
Frequently asked questions
What is the correct answer to this question?
-3
Why is this the correct answer?
The common difference of an arithmetic progression is the difference between two consecutive terms: second term − first term. Here, \(d=12-15=-3\), and the same value is obtained from \(9-12=-3\) and \(6-9=-3\). Therefore, option B, \(-3\), is correct. Since the progression is decreasing, its common difference is negative; writing only its magnitude, \(3\), would be incorrect. Exam tip: calculate \(a_2-a_1\) or subtract any term from the term immediately following it.
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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