If (3m,4m+2,6m-2) are in an arithmetic progression, what is the value of (m)?
Answer and explanation
Correct answer: 6
In an arithmetic progression, twice the middle term equals the sum of the first and third terms. Thus, \(2(4m+2)=3m+(6m-2)\). This gives \(8m+4=9m-2\), so \(m=6\). If 5 is substituted, the two consecutive differences are not equal. Exam tip: for three AP terms, use \(2b=a+c\) directly.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
In an arithmetic progression, twice the middle term equals the sum of the first and third terms. Thus, \(2(4m+2)=3m+(6m-2)\). This gives \(8m+4=9m-2\), so \(m=6\). If 5 is substituted, the two consecutive differences are not equal. Exam tip: for three AP terms, use \(2b=a+c\) directly.
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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