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Subjects
Class 10MathematicsArithmetic Progressions (AP)Finding the $n$th term of an APHardLevel 66

Which of the following sequences has an \(n\)th term that represents an arithmetic progression for every positive integer \(n\)?

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Answer and explanation

Correct answer: \(a_n=5n-2\)

The nth term of an AP has the linear form \(a_n=pn+q\), where \(p\) is the common difference. In option A, consecutive terms differ by \(5\). In option B, the differences are not constant. Exam tip: identify the linear form first.

Tags

arithmetic progressionnth termlinear sequencecommon differenceclass 10 mathematics

Frequently asked questions

What is the correct answer to this question?

\(a_n=5n-2\)

Why is this the correct answer?

The nth term of an AP has the linear form \(a_n=pn+q\), where \(p\) is the common difference. In option A, consecutive terms differ by \(5\). In option B, the differences are not constant. Exam tip: identify the linear form first.

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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