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

Which of the following nth-term formulas defines an arithmetic progression (AP) necessarily?

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Answer and explanation

Correct answer: \(a_n=5n-3\)

For \(a_n=5n-3\), \(a_{n+1}-a_n=5\), which is constant for every \(n\); hence it is an AP. In \(n^2+1\), successive differences vary. Exam tip: any linear form \(pn+q\) defines an AP.

Tags

arithmetic progressionnth termcommon differencelinear sequenceclass 10 mathematics

Frequently asked questions

What is the correct answer to this question?

\(a_n=5n-3\)

Why is this the correct answer?

For \(a_n=5n-3\), \(a_{n+1}-a_n=5\), which is constant for every \(n\); hence it is an AP. In \(n^2+1\), successive differences vary. Exam tip: any linear form \(pn+q\) defines an AP.

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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