What is the common difference in the sequence (5x,5x+2,5x+4,\ldots)?
Answer and explanation
Correct answer: (2)
The common difference is the amount added to one term to obtain the next term. With algebraic terms, the same rule is used: subtract the entire first term from the entire second term. Any variable parts that are identical cancel during subtraction, leaving the constant change between the terms.
Here the first term is \\(5x\\), and the second term is \\(5x+2\\). Thus, \\(d=(5x+2)-5x=2\\). The value of \\(x\\) does not matter because the two \\(5x\\) parts cancel. The third term also confirms the result: \\((5x+4)-(5x+2)=2\\). Therefore the sequence has common difference 2, so choice A is correct. Expressions such as \\(5x\\) or \\(5x+2\\) are terms, not the difference.
Frequently asked questions
What is the correct answer to this question?
(2)
Why is this the correct answer?
The common difference is the amount added to one term to obtain the next term. With algebraic terms, the same rule is used: subtract the entire first term from the entire second term. Any variable parts that are identical cancel during subtraction, leaving the constant change between the terms.
Here the first term is \\(5x\\), and the second term is \\(5x+2\\). Thus, \\(d=(5x+2)-5x=2\\). The value of \\(x\\) does not matter because the two \\(5x\\) parts cancel. The third term also confirms the result: \\((5x+4)-(5x+2)=2\\). Therefore the sequence has common difference 2, so choice A is correct. Expressions such as \\(5x\\) or \\(5x+2\\) are terms, not the difference.
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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