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

For the AP whose nth term is \(a_n=7-3n\), which statement is correct?

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Answer and explanation

Correct answer: It is a decreasing AP with common difference \(-3\).

Rewrite \(a_n=7-3n\) as \(4+(n-1)(-3)\), so the common difference is \(-3\). A negative difference makes the AP decreasing; \(3\) would give an increasing AP. Exam tip: identify \(d\) from the coefficient of \(n\).

Tags

arithmetic progressionnth termcommon differenceap propertiesclass 10 mathematics

Frequently asked questions

What is the correct answer to this question?

It is a decreasing AP with common difference \(-3\).

Why is this the correct answer?

Rewrite \(a_n=7-3n\) as \(4+(n-1)(-3)\), so the common difference is \(-3\). A negative difference makes the AP decreasing; \(3\) would give an increasing AP. Exam tip: identify \(d\) from the coefficient of \(n\).

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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