If (3, 3+2m, 3+4m, 3+6m) is an arithmetic progression, what is the common difference?
Answer and explanation
Correct answer: \(2m\)
Find the differences between consecutive terms: \((3+2m)-3=2m\), \((3+4m)-(3+2m)=2m\), and \((3+6m)-(3+4m)=2m\). Since every consecutive difference is the same, the common difference is \(2m\). \(m\) is not the increase between consecutive terms; subtract consecutive terms to obtain the difference. Exam tip: In an AP, verify using \(d=a_{n+1}-a_n\).
Frequently asked questions
What is the correct answer to this question?
\(2m\)
Why is this the correct answer?
Find the differences between consecutive terms: \((3+2m)-3=2m\), \((3+4m)-(3+2m)=2m\), and \((3+6m)-(3+4m)=2m\). Since every consecutive difference is the same, the common difference is \(2m\). \(m\) is not the increase between consecutive terms; subtract consecutive terms to obtain the difference. Exam tip: In an AP, verify using \(d=a_{n+1}-a_n\).
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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