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Subjects
Class 10MathematicsArithmetic Progressions (AP)Finding the $n$th term of an APExpertLevel 65

If the \(p\)th term of an AP is \(a_p\) and its common difference is \(d\), which relation correctly gives the \(n\)th term?

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Answer and explanation

Correct answer: \(a_n=a_p+(n-p)d\)

From the \(p\)th term to the \(n\)th term, the common difference is added \(n-p\) times, so \(a_n=a_p+(n-p)d\). Option C reverses the difference. Exam tip: count gaps between term positions, not the positions themselves.

Tags

arithmetic progressionnth termcommon differenceap formulasequence properties

Frequently asked questions

What is the correct answer to this question?

\(a_n=a_p+(n-p)d\)

Why is this the correct answer?

From the \(p\)th term to the \(n\)th term, the common difference is added \(n-p\) times, so \(a_n=a_p+(n-p)d\). Option C reverses the difference. Exam tip: count gaps between term positions, not the positions themselves.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.

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