If the nth term of a sequence is \(a_n=4n-9\), which correctly identifies it as an arithmetic progression (AP)?
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Answer and explanation
Correct answer: \(a_{n+1}-a_n=4\)
In an AP, the difference between consecutive terms is constant. Here, \(a_{n+1}-a_n=[4(n+1)-9]-(4n-9)=4\), so it is an AP. A constant ratio identifies a GP instead. Exam tip: check the coefficient of \(n\) for the common difference.
Frequently asked questions
What is the correct answer to this question?
\(a_{n+1}-a_n=4\)
Why is this the correct answer?
In an AP, the difference between consecutive terms is constant. Here, \(a_{n+1}-a_n=[4(n+1)-9]-(4n-9)=4\), so it is an AP. A constant ratio identifies a GP instead. Exam tip: check the coefficient of \(n\) for the common difference.
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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