The sequence (4x-3, 3x+5, x+21) is in an arithmetic progression. Which is the correct 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 \((3x+5)-(4x-3)=8-x\), and the third-minus-second difference is \((x+21)-(3x+5)=16-2x\). So, \(8-x=16-2x\), giving \(x=8\). The terms then become \(29,29,29\), so the common difference is \(0\). \(8\) is only an intermediate value obtained while solving, not the common difference. Exam tip: first equate consecutive differences to find the variable, then calculate the common difference.
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 are equal. Here, the second-minus-first difference is \((3x+5)-(4x-3)=8-x\), and the third-minus-second difference is \((x+21)-(3x+5)=16-2x\). So, \(8-x=16-2x\), giving \(x=8\). The terms then become \(29,29,29\), so the common difference is \(0\). \(8\) is only an intermediate value obtained while solving, not the common difference. Exam tip: first equate consecutive differences to find the variable, then calculate the common difference.
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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