The sequence (2, 2+k, 2+4k, 2+9k) can be an arithmetic progression. Under what condition?
Answer and explanation
Correct answer: \(k=0\)
In an arithmetic progression, the differences between consecutive terms must be equal. Here the differences are \(k\), \(3k\), and \(5k\). For them to be equal, \(k=3k=5k\), which is possible only when \(k=0\). Then the sequence becomes \(2,2,2,2\), with common difference \(0\). For example, when \(k=1\), the differences are \(1,3,5\), so it is not an AP. Exam tip: To test an AP, compare all consecutive differences.
Frequently asked questions
What is the correct answer to this question?
\(k=0\)
Why is this the correct answer?
In an arithmetic progression, the differences between consecutive terms must be equal. Here the differences are \(k\), \(3k\), and \(5k\). For them to be equal, \(k=3k=5k\), which is possible only when \(k=0\). Then the sequence becomes \(2,2,2,2\), with common difference \(0\). For example, when \(k=1\), the differences are \(1,3,5\), so it is not an AP. Exam tip: To test an AP, compare all consecutive differences.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..
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