Which sequence starts with (a=9) and (d=2)?
Answer and explanation
Correct answer: (9,11,13,15,\ldots)
An arithmetic progression is determined by two pieces of information: its first term \(a\) and its common difference \(d\). Starting with \(a=9\), add \(d=2\) repeatedly. This gives the pattern \(9, 9+2, 9+2+2, 9+2+2+2,\ldots\). Equivalently, its general term is \(a_n=a+(n-1)d\), so here \(a_n=9+2(n-1)\).
The first listed sequence is \(9,11,13,15,\ldots\). It begins with 9, and each consecutive difference is 2: \(11-9=2\), \(13-11=2\), and \(15-13=2\). Therefore choice A matches both requirements. Option C begins with 9 but has common difference 9, while option B begins with 2 and option D begins with 11, so none of those satisfies both conditions.
Frequently asked questions
What is the correct answer to this question?
(9,11,13,15,\ldots)
Why is this the correct answer?
An arithmetic progression is determined by two pieces of information: its first term \(a\) and its common difference \(d\). Starting with \(a=9\), add \(d=2\) repeatedly. This gives the pattern \(9, 9+2, 9+2+2, 9+2+2+2,\ldots\). Equivalently, its general term is \(a_n=a+(n-1)d\), so here \(a_n=9+2(n-1)\).
The first listed sequence is \(9,11,13,15,\ldots\). It begins with 9, and each consecutive difference is 2: \(11-9=2\), \(13-11=2\), and \(15-13=2\). Therefore choice A matches both requirements. Option C begins with 9 but has common difference 9, while option B begins with 2 and option D begins with 11, so none of those satisfies both conditions.
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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