Which of the following conditions is necessary and sufficient to identify a sequence as an arithmetic progression (AP) from its nth term \(a_n\)?
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Answer and explanation
Correct answer: \(a_{n+1}-a_n\) is the same constant for every positive integer \(n\)
In an AP, the difference of consecutive terms is the common difference \(d\), so \(a_{n+1}-a_n=d\) must be constant. A constant ratio instead identifies a GP. Exam tip: subtract two consecutive nth-term expressions to test for an AP.
Frequently asked questions
What is the correct answer to this question?
\(a_{n+1}-a_n\) is the same constant for every positive integer \(n\)
Why is this the correct answer?
In an AP, the difference of consecutive terms is the common difference \(d\), so \(a_{n+1}-a_n=d\) must be constant. A constant ratio instead identifies a GP. Exam tip: subtract two consecutive nth-term expressions to test for an AP.
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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