The sequence (4x-3, 3x+5, x+21) is in an arithmetic progression. What is the common difference?
Answer and explanation
Correct answer: 0
In an arithmetic progression, the differences between consecutive terms are equal. Here, the second-minus-first difference is \((3x+5)-(4x-3)=-x+8\), and the third-minus-second difference is \((x+21)-(3x+5)=-2x+16\). Equating them gives \(-x+8=-2x+16\), so \(x=8\). The terms then become \(29,29,29\), making the common difference \(0\). Option 8 is the value of \(x\), not the common difference. Exam tip: first equate consecutive differences to find the variable, then substitute it to obtain \(d\).
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What is the correct answer to this question?
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Why is this the correct answer?
In an arithmetic progression, the differences between consecutive terms are equal. Here, the second-minus-first difference is \((3x+5)-(4x-3)=-x+8\), and the third-minus-second difference is \((x+21)-(3x+5)=-2x+16\). Equating them gives \(-x+8=-2x+16\), so \(x=8\). The terms then become \(29,29,29\), making the common difference \(0\). Option 8 is the value of \(x\), not the common difference. Exam tip: first equate consecutive differences to find the variable, then substitute it to obtain \(d\).
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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