If (x − 2, 2x + 1, 4x − 3) are consecutive terms of an AP, what are x and d?
Answer and explanation
Correct answer: x = 7, d = 10
For three consecutive terms of an arithmetic progression, the two consecutive differences must be equal. The first difference is (2x + 1) − (x − 2) = x + 3. The second difference is (4x − 3) − (2x + 1) = 2x − 4. Equating them gives x + 3 = 2x − 4, so x = 7. Substituting this value, the first difference is 7 + 3 = 10, and the second difference is 14 − 4 = 10 as well. Hence d = 10 and option C is correct. The other choices fail because their values of x do not make the two differences equal.
Frequently asked questions
What is the correct answer to this question?
x = 7, d = 10
Why is this the correct answer?
For three consecutive terms of an arithmetic progression, the two consecutive differences must be equal. The first difference is (2x + 1) − (x − 2) = x + 3. The second difference is (4x − 3) − (2x + 1) = 2x − 4. Equating them gives x + 3 = 2x − 4, so x = 7. Substituting this value, the first difference is 7 + 3 = 10, and the second difference is 14 − 4 = 10 as well. Hence d = 10 and option C is correct. The other choices fail because their values of x do not make the two 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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