If (6, h, 30) are in an arithmetic progression, which pair of (h) and common difference is correct?
Answer and explanation
Correct answer: \(h=18,\ d=12\)
For three terms in an arithmetic progression, the middle term is the average of the first and third terms. Thus, \(h=\frac{6+30}{2}=18\). Hence the common difference is \(d=18-6=12\), and also \(30-18=12\). In option A, the two consecutive differences are not equal. Exam tip: For a three-term AP, quickly find the middle term by averaging the first and third terms.
Frequently asked questions
What is the correct answer to this question?
\(h=18,\ d=12\)
Why is this the correct answer?
For three terms in an arithmetic progression, the middle term is the average of the first and third terms. Thus, \(h=\frac{6+30}{2}=18\). Hence the common difference is \(d=18-6=12\), and also \(30-18=12\). In option A, the two consecutive differences are not equal. Exam tip: For a three-term AP, quickly find the middle term by averaging 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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