Which of the following rules represents the \(n\)th term of an arithmetic progression for every positive integer \(n\)?
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Answer and explanation
Correct answer: \(a_n=5-3n\)
For option B, \(a_{n+1}-a_n=[5-3(n+1)]-(5-3n)=-3\), which is constant for every \(n\). Hence it is an AP. In option A, the difference depends on \(n\). Exam tip: test \(a_{n+1}-a_n\) for constancy.
Frequently asked questions
What is the correct answer to this question?
\(a_n=5-3n\)
Why is this the correct answer?
For option B, \(a_{n+1}-a_n=[5-3(n+1)]-(5-3n)=-3\), which is constant for every \(n\). Hence it is an AP. In option A, the difference depends on \(n\). Exam tip: test \(a_{n+1}-a_n\) for constancy.
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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