If a, b, c are in arithmetic progression and a = 6, c = 30, what is b − a?
Answer and explanation
Correct answer: 12
For three consecutive terms in an arithmetic progression, the middle term is the average of the first and third terms. Thus b = (a + c)/2 = (6 + 30)/2 = 36/2 = 18. The required quantity is not b itself but b − a, so b − a = 18 − 6 = 12. Equivalently, the total difference from 6 to 30 is 24, and it consists of two equal AP gaps; each gap is 24/2 = 12. Therefore option B is correct. Option C is the middle term b, while option D is the full end-to-end difference and option A does not follow from the AP condition.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
For three consecutive terms in an arithmetic progression, the middle term is the average of the first and third terms. Thus b = (a + c)/2 = (6 + 30)/2 = 36/2 = 18. The required quantity is not b itself but b − a, so b − a = 18 − 6 = 12. Equivalently, the total difference from 6 to 30 is 24, and it consists of two equal AP gaps; each gap is 24/2 = 12. Therefore option B is correct. Option C is the middle term b, while option D is the full end-to-end difference and option A does not follow from the AP condition.
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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
