If (2a−5, a+4, 4a−7) are in an arithmetic progression, what is the value of a?
Answer and explanation
Correct answer: 5
For three terms in an arithmetic progression, the middle term is the average of the first and third. Therefore, 2(a+4)=(2a−5)+(4a−7). Simplifying the left side gives 2a+8, while the right side gives 6a−12. Thus 2a+8=6a−12, so 20=4a and a=5. Substitution produces the terms 5, 9, and 13, whose consecutive differences are both 4. Hence option D is correct. The other values fail the equality of the two consecutive differences and are only distractors.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
For three terms in an arithmetic progression, the middle term is the average of the first and third. Therefore, 2(a+4)=(2a−5)+(4a−7). Simplifying the left side gives 2a+8, while the right side gives 6a−12. Thus 2a+8=6a−12, so 20=4a and a=5. Substitution produces the terms 5, 9, and 13, whose consecutive differences are both 4. Hence option D is correct. The other values fail the equality of the two consecutive differences and are only distractors.
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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