If (13, 2x+1, 4x-5) are in an arithmetic progression, what is the common difference?
Answer and explanation
Correct answer: No such common difference exists
In an arithmetic progression, the middle term is the average of the first and third terms. Therefore, \(2(2x+1)=13+(4x-5)\) must hold. Simplifying gives \(4x+2=4x+8\), or \(2=8\), which is impossible. Hence, for no value of \(x\) do these three terms form an AP, so no common difference exists. Exam tip: for three terms \(a,b,c\), check an AP quickly using \(2b=a+c\).
Frequently asked questions
What is the correct answer to this question?
No such common difference exists
Why is this the correct answer?
In an arithmetic progression, the middle term is the average of the first and third terms. Therefore, \(2(2x+1)=13+(4x-5)\) must hold. Simplifying gives \(4x+2=4x+8\), or \(2=8\), which is impossible. Hence, for no value of \(x\) do these three terms form an AP, so no common difference exists. Exam tip: for three terms \(a,b,c\), check an AP quickly using \(2b=a+c\).
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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