For which value of k will (k−3, k+2, 2k+1) be in an arithmetic progression?
Answer and explanation
Correct answer: 6
The governing concept is the middle-term condition for three consecutive terms of an arithmetic progression: twice the middle term equals the sum of the first and third terms. Therefore, 2(k + 2) = (k − 3) + (2k + 1). On simplifying, 2k + 4 = 3k − 2, so k = 6. Substitution provides an independent check: the three terms become 3, 8, and 13. Their consecutive differences are 8 − 3 = 5 and 13 − 8 = 5, so the difference is constant and the sequence is an AP. Hence option C is correct. Values such as 5 or 7 can result from an algebraic sign or rearrangement error, but they do not make both consecutive differences equal.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The governing concept is the middle-term condition for three consecutive terms of an arithmetic progression: twice the middle term equals the sum of the first and third terms. Therefore, 2(k + 2) = (k − 3) + (2k + 1). On simplifying, 2k + 4 = 3k − 2, so k = 6. Substitution provides an independent check: the three terms become 3, 8, and 13. Their consecutive differences are 8 − 3 = 5 and 13 − 8 = 5, so the difference is constant and the sequence is an AP. Hence option C is correct. Values such as 5 or 7 can result from an algebraic sign or rearrangement error, but they do not make both consecutive differences equal.
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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