Which statement is correct about the sequence (3,3,3,3,\ldots)?
Answer and explanation
Correct answer: It is an arithmetic progression and (d=0)
An arithmetic progression is a sequence in which the difference between consecutive terms remains constant. In the sequence \(3,3,3,3,\ldots\), subtracting one term from the next gives \(3-3=0\) every time. Therefore the common difference is \(d=0\). The fact that the terms do not increase or decrease does not disqualify the sequence from being an arithmetic progression.
The first term is \(a=3\), not zero. Thus the correct statement is option B: it is an arithmetic progression with common difference zero. A constant sequence is an important special case of an arithmetic progression. The value 3 is the repeated term, while 0 describes the change between successive terms.
Frequently asked questions
What is the correct answer to this question?
It is an arithmetic progression and (d=0)
Why is this the correct answer?
An arithmetic progression is a sequence in which the difference between consecutive terms remains constant. In the sequence \(3,3,3,3,\ldots\), subtracting one term from the next gives \(3-3=0\) every time. Therefore the common difference is \(d=0\). The fact that the terms do not increase or decrease does not disqualify the sequence from being an arithmetic progression.
The first term is \(a=3\), not zero. Thus the correct statement is option B: it is an arithmetic progression with common difference zero. A constant sequence is an important special case of an arithmetic progression. The value 3 is the repeated term, while 0 describes the change between successive terms.
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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