For which (m) will (m-1,2m+3,4m-1) be in an arithmetic progression?
Answer and explanation
Correct answer: 8
For three terms to be in an AP, twice the middle term must equal the sum of the first and third terms. Thus, \(2(2m+3)=(m-1)+(4m-1)\). This gives \(4m+6=5m-2\), so \(m=8\). A nearby option such as \(m=6\) does not satisfy this equality. Exam tip: for three AP terms, directly use \(2b=a+c\).
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
For three terms to be in an AP, twice the middle term must equal the sum of the first and third terms. Thus, \(2(2m+3)=(m-1)+(4m-1)\). This gives \(4m+6=5m-2\), so \(m=8\). A nearby option such as \(m=6\) does not satisfy this equality. Exam tip: for three AP terms, directly use \(2b=a+c\).
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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