If (x, x+6, 3x-2) are in an arithmetic progression, what is the correct value of (x)?
Answer and explanation
Correct answer: 7
In an arithmetic progression, the differences between consecutive terms are equal. Here, the difference between the second and first terms is \((x+6)-x=6\), while that between the third and second terms is \((3x-2)-(x+6)=2x-8\). Therefore, \(2x-8=6\), so \(2x=14\) and \(x=7\). If \(x=6\), the second difference becomes 4, not 6. Exam tip: For three AP terms, you can also use \(2\times\) middle term = first term + third term.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
In an arithmetic progression, the differences between consecutive terms are equal. Here, the difference between the second and first terms is \((x+6)-x=6\), while that between the third and second terms is \((3x-2)-(x+6)=2x-8\). Therefore, \(2x-8=6\), so \(2x=14\) and \(x=7\). If \(x=6\), the second difference becomes 4, not 6. Exam tip: For three AP terms, you can also use \(2\times\) middle term = first term + third term.
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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