The first term of an AP is x, and the common difference is 3x − 2. If the sum of the first 12 terms is 1128, what is the value of x?
Answer and explanation
Correct answer: 6
Use Sₙ = n/2[2a + (n − 1)d] with n = 12, a = x, and d = 3x − 2. Then 1128 = 12/2[2x + 11(3x − 2)] = 6[2x + 33x − 22] = 6(35x − 22). Dividing by 6 gives 188 = 35x − 22, so 35x = 210 and x = 6. Therefore option B is correct. After finding x, the common difference would be 3(6) − 2 = 16, which is consistent with the equation but is not needed separately. The other options result from forgetting the factor 11, distributing incorrectly, or treating d as independent of x.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
Use Sₙ = n/2[2a + (n − 1)d] with n = 12, a = x, and d = 3x − 2. Then 1128 = 12/2[2x + 11(3x − 2)] = 6[2x + 33x − 22] = 6(35x − 22). Dividing by 6 gives 188 = 35x − 22, so 35x = 210 and x = 6. Therefore option B is correct. After finding x, the common difference would be 3(6) − 2 = 16, which is consistent with the equation but is not needed separately. The other options result from forgetting the factor 11, distributing incorrectly, or treating d as independent of x.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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