If (p-4, 2p+1, 4p-2) are in an arithmetic progression, what will be the common difference?
Answer and explanation
Correct answer: 13
In an arithmetic progression, the differences between consecutive terms are equal. Therefore,
\((2p+1)-(p-4)=(4p-2)-(2p+1)\).
This gives \(p+5=2p-3\), so \(p=8\). The common difference is then \((2p+1)-(p-4)=17-4=13\). Values such as 15 do not equal the consecutive difference of the given terms. Exam tip: for three terms in an AP, set twice the middle term equal to the sum of the first and third terms.
Frequently asked questions
What is the correct answer to this question?
13
Why is this the correct answer?
In an arithmetic progression, the differences between consecutive terms are equal. Therefore,
\((2p+1)-(p-4)=(4p-2)-(2p+1)\).
This gives \(p+5=2p-3\), so \(p=8\). The common difference is then \((2p+1)-(p-4)=17-4=13\). Values such as 15 do not equal the consecutive difference of the given terms. Exam tip: for three terms in an AP, set twice the middle term equal to the sum of the first and third terms.
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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