If S_n = 3n^2 + 2n, what is the sum of the first 12 terms?
Answer and explanation
Correct answer: 456
The expression S_n directly gives the sum of the first n terms of the sequence, so no separate common difference or nth-term calculation is needed. Substitute n = 12: S_12 = 3(12)^2 + 2(12) = 3 × 144 + 24 = 432 + 24 = 456. Therefore, option B is correct. Option A, 452, could result from an arithmetic subtraction error; option C, 460, does not follow from the given expression; and option D, 468, may arise from adding 36 instead of 24. The governing concept is direct substitution into the formula for the sum of the first n terms.
Frequently asked questions
What is the correct answer to this question?
456
Why is this the correct answer?
The expression S_n directly gives the sum of the first n terms of the sequence, so no separate common difference or nth-term calculation is needed. Substitute n = 12: S_12 = 3(12)^2 + 2(12) = 3 × 144 + 24 = 432 + 24 = 456. Therefore, option B is correct. Option A, 452, could result from an arithmetic subtraction error; option C, 460, does not follow from the given expression; and option D, 468, may arise from adding 36 instead of 24. The governing concept is direct substitution into the formula for the sum of the first n terms.
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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