For which (a) is (a+4, 2a+1, 5a-8) an arithmetic progression?
Answer and explanation
Correct answer: 3
In an arithmetic progression, the differences between consecutive terms are equal. Here, the first difference is \((2a+1)-(a+4)=a-3\), and the second difference is \((5a-8)-(2a+1)=3a-9\). Thus, \(a-3=3a-9\), which gives \(a=3\). Therefore, option 3 is correct. Exam tip: For three terms to be an AP, equate the first and second differences.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
In an arithmetic progression, the differences between consecutive terms are equal. Here, the first difference is \((2a+1)-(a+4)=a-3\), and the second difference is \((5a-8)-(2a+1)=3a-9\). Thus, \(a-3=3a-9\), which gives \(a=3\). Therefore, option 3 is correct. Exam tip: For three terms to be an AP, equate the first and second 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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