For which value of k will k − 2, k + 5, 2k + 1 be in an arithmetic progression?
Answer and explanation
Correct answer: 11
For three quantities to be consecutive terms of an arithmetic progression, twice the middle term must equal the sum of the first and third terms. Here this gives 2(k + 5) = (k − 2) + (2k + 1). Expanding, 2k + 10 = 3k − 1, so k = 11. A direct check gives the terms 9, 16, 23, whose successive differences are 7 and 7, confirming the result. Therefore option D is correct. The earlier option value 9 was not valid because substituting k = 9 gives 7, 14, 19, with unequal differences 7 and 5; it has been corrected to 11.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
For three quantities to be consecutive terms of an arithmetic progression, twice the middle term must equal the sum of the first and third terms. Here this gives 2(k + 5) = (k − 2) + (2k + 1). Expanding, 2k + 10 = 3k − 1, so k = 11. A direct check gives the terms 9, 16, 23, whose successive differences are 7 and 7, confirming the result. Therefore option D is correct. The earlier option value 9 was not valid because substituting k = 9 gives 7, 14, 19, with unequal differences 7 and 5; it has been corrected to 11.
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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