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

If (a_6=31) and (a_{14}=79), what is the common difference of the AP?

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Answer and explanation

Correct answer: 6

For an AP, \(a_{14}-a_6=(14-6)d\). Thus, \(79-31=8d\), so \(48=8d\) and \(d=6\). If the common difference were 4, the difference over 8 positions would be only 32, not the given 48. Exam tip: when two non-consecutive terms are given, divide the difference of the terms by the difference of their indices.

Tags

arithmetic progressioncommon differencenth termclass 10 mathematicsalgebra

Frequently asked questions

What is the correct answer to this question?

6

Why is this the correct answer?

For an AP, \(a_{14}-a_6=(14-6)d\). Thus, \(79-31=8d\), so \(48=8d\) and \(d=6\). If the common difference were 4, the difference over 8 positions would be only 32, not the given 48. Exam tip: when two non-consecutive terms are given, divide the difference of the terms by the difference of their indices.

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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