If (9,b,21) are consecutive terms of an arithmetic progression, what is the value of (b)?
Answer and explanation
Correct answer: 15
For three consecutive terms of an arithmetic progression, the middle term equals the average of the first and third terms. Thus, \(b=\frac{9+21}{2}=15\). Therefore, 15 is the correct option. For instance, if \(b=13\), the differences are \(13-9=4\) and \(21-13=8\), which are not equal. Exam tip: For three consecutive AP terms \(a-d,\ a,\ a+d\), the middle term is always the average of the outer terms.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
For three consecutive terms of an arithmetic progression, the middle term equals the average of the first and third terms. Thus, \(b=\frac{9+21}{2}=15\). Therefore, 15 is the correct option. For instance, if \(b=13\), the differences are \(13-9=4\) and \(21-13=8\), which are not equal. Exam tip: For three consecutive AP terms \(a-d,\ a,\ a+d\), the middle term is always the average of the outer 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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