If (4p+1, 6p-3, 9p-10) are in an arithmetic progression, which pair of (p) and common difference is correct?
Answer and explanation
Correct answer: \(p=3,\ d=2\)
In an arithmetic progression, the differences between consecutive terms are equal. Here, the difference between the second and first terms is \((6p-3)-(4p+1)=2p-4\), while that between the third and second terms is \((9p-10)-(6p-3)=3p-7\). Thus, \(2p-4=3p-7\), giving \(p=3\). Substituting this value, \(d=2p-4=2\). For option C, putting \(p=4\) does not make the two differences equal. Exam tip: In AP questions, equate the two consecutive differences first.
Frequently asked questions
What is the correct answer to this question?
\(p=3,\ d=2\)
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 \((6p-3)-(4p+1)=2p-4\), while that between the third and second terms is \((9p-10)-(6p-3)=3p-7\). Thus, \(2p-4=3p-7\), giving \(p=3\). Substituting this value, \(d=2p-4=2\). For option C, putting \(p=4\) does not make the two differences equal. Exam tip: In AP questions, equate the two consecutive differences first.
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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