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

For the terms of any arithmetic progression (AP), which of the following relations is always true?

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Answer and explanation

Correct answer: \(a_7+a_{19}=2a_{13}\)

Using \(a_n=a+(n-1)d\), \(a_7+a_{19}=(a+6d)+(a+18d)=2a_{13}\). So option A is always true; B has the wrong middle term. Exam tip: pair terms equidistant from the centre.

Tags

arithmetic progressionnth termap propertiesterm relationsmathematics class 10

Frequently asked questions

What is the correct answer to this question?

\(a_7+a_{19}=2a_{13}\)

Why is this the correct answer?

Using \(a_n=a+(n-1)d\), \(a_7+a_{19}=(a+6d)+(a+18d)=2a_{13}\). So option A is always true; B has the wrong middle term. Exam tip: pair terms equidistant from the centre.

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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