If 6, h, 24 are in an arithmetic progression, what is h − 6?
Answer and explanation
Correct answer: 9
In three consecutive terms of an arithmetic progression, the middle term equals the average of the first and last terms. Therefore h = (6 + 24)/2 = 30/2 = 15. The question asks for the distance from the first term to the middle term, so h − 6 = 15 − 6 = 9. This also follows by observing that the total change 24 − 6 = 18 is divided into two equal common differences, each equal to 9. Hence the sequence is 6, 15, 24, and option B is correct. Option C is the total change, not one common difference.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
In three consecutive terms of an arithmetic progression, the middle term equals the average of the first and last terms. Therefore h = (6 + 24)/2 = 30/2 = 15. The question asks for the distance from the first term to the middle term, so h − 6 = 15 − 6 = 9. This also follows by observing that the total change 24 − 6 = 18 is divided into two equal common differences, each equal to 9. Hence the sequence is 6, 15, 24, and option B is correct. Option C is the total change, not one common difference.
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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