If (a,b,c) are in an arithmetic progression and (a=4), (c=22), what is (b-a)?
Answer and explanation
Correct answer: 9
In an arithmetic progression, the difference between consecutive terms is constant. Therefore, for three terms, the middle term b is the average of a and c: \(b=\frac{a+c}{2}=\frac{4+22}{2}=13\). Hence, \(b-a=13-4=9\). Option 11 can result from using an incorrect difference instead of halving \(c-a=22-4\). Exam tip: For three consecutive AP terms, the middle term is always the average of the first and third terms.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
In an arithmetic progression, the difference between consecutive terms is constant. Therefore, for three terms, the middle term b is the average of a and c: \(b=\frac{a+c}{2}=\frac{4+22}{2}=13\). Hence, \(b-a=13-4=9\). Option 11 can result from using an incorrect difference instead of halving \(c-a=22-4\). Exam tip: For three consecutive AP terms, the middle term is always the average of the first and third 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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