What is the common difference of (5m,5m-4,5m-8,5m-12,\ldots)?
Answer and explanation
Correct answer: (-4)
To find the common difference of an algebraic arithmetic progression, subtract one term from the next. Like terms cancel in the same way as ordinary numbers. If the result is negative, each successive term is smaller than the previous one by the absolute value of that negative number.
Using the first two terms, \\(d=(5m-4)-5m=-4\\). The same result appears again: \\((5m-8)-(5m-4)=-4\\), and \\((5m-12)-(5m-8)=-4\\). Thus the expression has a constant difference, so it is an arithmetic progression with common difference \\(-4\\). The variable part \\(5m\\) cancels; it is not the answer. Therefore choice B is correct.
Frequently asked questions
What is the correct answer to this question?
(-4)
Why is this the correct answer?
To find the common difference of an algebraic arithmetic progression, subtract one term from the next. Like terms cancel in the same way as ordinary numbers. If the result is negative, each successive term is smaller than the previous one by the absolute value of that negative number.
Using the first two terms, \\(d=(5m-4)-5m=-4\\). The same result appears again: \\((5m-8)-(5m-4)=-4\\), and \\((5m-12)-(5m-8)=-4\\). Thus the expression has a constant difference, so it is an arithmetic progression with common difference \\(-4\\). The variable part \\(5m\\) cancels; it is not the answer. Therefore choice B 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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