If (2u−1, 3u+2, 5u+1) are in an arithmetic progression, what is the value of u?
Answer and explanation
Correct answer: 4
For three numbers to be consecutive terms of an arithmetic progression, the middle term is the arithmetic mean of the first and third. Thus twice the middle term equals the sum of the outer terms: 2(3u + 2) = (2u − 1) + (5u + 1). Expanding gives 6u + 4 = 7u, so u = 4. Substitution provides a complete check: the three terms become 7, 14, and 21. Their consecutive differences are 14 − 7 = 7 and 21 − 14 = 7, so they do form an AP. Therefore option D is correct. The other listed values do not make the two consecutive differences equal and hence cannot satisfy the AP condition.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For three numbers to be consecutive terms of an arithmetic progression, the middle term is the arithmetic mean of the first and third. Thus twice the middle term equals the sum of the outer terms: 2(3u + 2) = (2u − 1) + (5u + 1). Expanding gives 6u + 4 = 7u, so u = 4. Substitution provides a complete check: the three terms become 7, 14, and 21. Their consecutive differences are 14 − 7 = 7 and 21 − 14 = 7, so they do form an AP. Therefore option D is correct. The other listed values do not make the two consecutive differences equal and hence cannot satisfy 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.
