What is the common difference of the arithmetic progression (a-2,a+1,a+4,a+7,\ldots)?
Answer and explanation
Correct answer: \(3\)
The common difference of an AP is found by subtracting a term from the term immediately after it. Here, \((a+1)-(a-2)=a+1-a+2=3\). Also, \((a+4)-(a+1)=3\), so the common difference is \(3\). \(a+3\) could represent a term, not the difference. Exam tip: When subtracting algebraic expressions, use brackets carefully to handle signs correctly.
Frequently asked questions
What is the correct answer to this question?
\(3\)
Why is this the correct answer?
The common difference of an AP is found by subtracting a term from the term immediately after it. Here, \((a+1)-(a-2)=a+1-a+2=3\). Also, \((a+4)-(a+1)=3\), so the common difference is \(3\). \(a+3\) could represent a term, not the difference. Exam tip: When subtracting algebraic expressions, use brackets carefully to handle signs correctly.
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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