Which of the following nth-term expressions defines an arithmetic progression (AP) for every positive integer \(n\)?
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Answer and explanation
Correct answer: \(a_n=\frac{5-2n}{3}\)
For option A, \(a_{n+1}-a_n=\frac{5-2(n+1)}{3}-\frac{5-2n}{3}=-\frac{2}{3}\), which is constant; hence it is an AP. In B, the difference changes. Exam tip: an AP has an nth term linear in \(n\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=\frac{5-2n}{3}\)
Why is this the correct answer?
For option A, \(a_{n+1}-a_n=\frac{5-2(n+1)}{3}-\frac{5-2n}{3}=-\frac{2}{3}\), which is constant; hence it is an AP. In B, the difference changes. Exam tip: an AP has an nth term linear in \(n\).
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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