Which of the following nth-term expressions represents an arithmetic progression (AP)?
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Answer and explanation
Correct answer: \(a_n=7-3n\)
For \(a_n=7-3n\), \(a_{n+1}-a_n=[7-3(n+1)]-(7-3n)=-3\), which is constant for every \(n\). Hence it is an AP. In option B, the difference is \(2n-2\), so it changes. Exam tip: test whether consecutive-term differences are constant.
Frequently asked questions
What is the correct answer to this question?
\(a_n=7-3n\)
Why is this the correct answer?
For \(a_n=7-3n\), \(a_{n+1}-a_n=[7-3(n+1)]-(7-3n)=-3\), which is constant for every \(n\). Hence it is an AP. In option B, the difference is \(2n-2\), so it changes. Exam tip: test whether consecutive-term differences are constant.
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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