Three consecutive terms of an arithmetic progression are 4x - 1, 5x + 2, and 7x - 3. What is x?
Answer and explanation
Correct answer: 8
For three consecutive terms of an arithmetic progression, the middle term is the arithmetic mean of the first and third. Therefore 2(5x + 2) = (4x - 1) + (7x - 3). Expanding gives 10x + 4 = 11x - 4, so x = 8. Substitution verifies the terms: 4(8) - 1 = 31, 5(8) + 2 = 42, and 7(8) - 3 = 53; the two successive differences are 11 and 11. Hence option D is correct. The original option set did not contain 8 and its marked answer was inconsistent, so the final option set has been corrected. Values 4, 5, and 6 fail the equal-difference condition.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
For three consecutive terms of an arithmetic progression, the middle term is the arithmetic mean of the first and third. Therefore 2(5x + 2) = (4x - 1) + (7x - 3). Expanding gives 10x + 4 = 11x - 4, so x = 8. Substitution verifies the terms: 4(8) - 1 = 31, 5(8) + 2 = 42, and 7(8) - 3 = 53; the two successive differences are 11 and 11. Hence option D is correct. The original option set did not contain 8 and its marked answer was inconsistent, so the final option set has been corrected. Values 4, 5, and 6 fail the equal-difference condition.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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