Is the sequence (3,7,12,18,\ldots) an arithmetic progression or not?
Answer and explanation
Correct answer: No, because the differences between consecutive terms are not equal
The differences between consecutive terms are \(7-3=4\), \(12-7=5\), and \(18-12=6\). In an arithmetic progression, every consecutive difference must be the same, but here the differences are 4, 5, and 6. Therefore, this is not an arithmetic progression. Merely increasing terms do not make a sequence an AP. Exam tip: To check an AP, compare at least two or three consecutive differences.
Frequently asked questions
What is the correct answer to this question?
No, because the differences between consecutive terms are not equal
Why is this the correct answer?
The differences between consecutive terms are \(7-3=4\), \(12-7=5\), and \(18-12=6\). In an arithmetic progression, every consecutive difference must be the same, but here the differences are 4, 5, and 6. Therefore, this is not an arithmetic progression. Merely increasing terms do not make a sequence an AP. Exam tip: To check an AP, compare at least two or three 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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