If (a, b, c) are in an arithmetic progression, what is the value of (a-2b+c)?
Answer and explanation
Correct answer: 0
In an arithmetic progression, consecutive differences are equal: b-a=c-b. Rearranging gives a+c=2b. Hence, a-2b+c=a+c-2b=0. A common mistake is to focus only on the difference; the middle term is always the average of the first and third terms. Exam tip: for three AP terms, use 2b=a+c directly.
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Why is this the correct answer?
In an arithmetic progression, consecutive differences are equal: b-a=c-b. Rearranging gives a+c=2b. Hence, a-2b+c=a+c-2b=0. A common mistake is to focus only on the difference; the middle term is always the average of the first and third terms. Exam tip: for three AP terms, use 2b=a+c directly.
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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