For which (n) will (n+2, 2n+5, 4n+8) form an arithmetic progression?
Answer and explanation
Correct answer: \(0\)
In an arithmetic progression, the differences between consecutive terms must be equal. Here, the difference between the second and first terms is \((2n+5)-(n+2)=n+3\), while the difference between the third and second terms is \((4n+8)-(2n+5)=2n+3\). Thus, \(n+3=2n+3\), giving \(n=0\). On substituting \(n=0\), the terms are \(2,5,8\), with common difference \(3\). For example, at \(n=1\), the differences are \(4\) and \(5\), so it is not an AP. Exam tip: For three terms to form an AP, equate the two consecutive differences.
Frequently asked questions
What is the correct answer to this question?
\(0\)
Why is this the correct answer?
In an arithmetic progression, the differences between consecutive terms must be equal. Here, the difference between the second and first terms is \((2n+5)-(n+2)=n+3\), while the difference between the third and second terms is \((4n+8)-(2n+5)=2n+3\). Thus, \(n+3=2n+3\), giving \(n=0\). On substituting \(n=0\), the terms are \(2,5,8\), with common difference \(3\). For example, at \(n=1\), the differences are \(4\) and \(5\), so it is not an AP. Exam tip: For three terms to form an AP, equate the two consecutive differences.
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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