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

Which of the following rules defines the nth term of an arithmetic progression for every positive integer n?

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Answer and explanation

Correct answer: \(a_n=7n-3\)

For \(a_n=7n-3\), \(a_{n+1}-a_n=[7(n+1)-3]-(7n-3)=7\), a constant difference; hence it is an AP. In \(n^2+7\), the differences vary. Exam tip: a linear expression in n represents an AP.

Tags

arithmetic progressionnth termcommon differencelinear sequencemathematics class 10

Frequently asked questions

What is the correct answer to this question?

\(a_n=7n-3\)

Why is this the correct answer?

For \(a_n=7n-3\), \(a_{n+1}-a_n=[7(n+1)-3]-(7n-3)=7\), a constant difference; hence it is an AP. In \(n^2+7\), the differences vary. Exam tip: a linear expression in n represents 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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