The \(n\)th term of a sequence is \(a_n=4n-7\). What is the most appropriate reason for identifying it as an arithmetic progression (AP)?
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Answer and explanation
Correct answer: For every \(n\), \(a_{n+1}-a_n=4\), which is constant.
\(a_{n+1}-a_n=[4(n+1)-7]-(4n-7)=4\). A sequence is an AP only when consecutive terms have a constant difference. A negative first term does not prove this. Exam tip: test \(a_{n+1}-a_n\).
Frequently asked questions
What is the correct answer to this question?
For every \(n\), \(a_{n+1}-a_n=4\), which is constant.
Why is this the correct answer?
\(a_{n+1}-a_n=[4(n+1)-7]-(4n-7)=4\). A sequence is an AP only when consecutive terms have a constant difference. A negative first term does not prove this. Exam tip: test \(a_{n+1}-a_n\).
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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