Which of the following sequences has the same difference between every pair of consecutive terms and is therefore an arithmetic progression (AP)?
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Answer and explanation
Correct answer: \(a_n=5n-2\)
For option A, \(a_{n+1}-a_n=[5(n+1)-2]-(5n-2)=5\), which is constant for every \(n\); hence it is an AP. In option B, the difference changes. Exam tip: test consecutive differences first.
Frequently asked questions
What is the correct answer to this question?
\(a_n=5n-2\)
Why is this the correct answer?
For option A, \(a_{n+1}-a_n=[5(n+1)-2]-(5n-2)=5\), which is constant for every \(n\); hence it is an AP. In option B, the difference changes. Exam tip: test consecutive differences first.
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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