Which of the following nth-term rules represents an arithmetic progression with common difference \(-2\)?
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Answer and explanation
Correct answer: \(a_n=5-2n\)
For \(a_n=5-2n\), \(a_{n+1}-a_n=[5-2(n+1)]-(5-2n)=-2\), which is constant for every n. Hence it is an AP. The differences for \(3n^2-2\) are not constant. Exam tip: in \(a_n=pn+q\), the common difference is \(p\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=5-2n\)
Why is this the correct answer?
For \(a_n=5-2n\), \(a_{n+1}-a_n=[5-2(n+1)]-(5-2n)=-2\), which is constant for every n. Hence it is an AP. The differences for \(3n^2-2\) are not constant. Exam tip: in \(a_n=pn+q\), the common difference is \(p\).
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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