If in an AP (S_{24}=1560) and (S_{12}=456), what is the sum from the (13)th term to the (24)th term?

Correct answer: (1104)

The direct answer is option B: 1104. S24 means the sum of the first 24 terms, while S12 means the sum of the first 12 terms. The first 24 terms consist of the first 12 terms plus terms 13 through 24. Therefore, to remove the first 12 terms, subtract the two partial sums: sum from the 13th term to the 24th term = S24−S12. Substitute the given values: 1560−456=1104. Hence option B is correct. Option A, 1080, is wrong because it comes from an incorrect subtraction or an incomplete interpretation of the requested range. Option B is correct because subtracting the first 12-term total from the first 24-term total leaves exactly terms 13 to 24. Option C, 1128, is wrong because it is not the difference of the supplied partial sums. Option D, 1152, is also wrong for the same reason and may result from reversing or altering the numbers. No value of a or d is needed; the question directly gives the required partial sums. The key idea is that a later block of consecutive terms can be isolated by subtracting earlier partial sums. Memory cue: “from r to s = Ss−S(r−1).” Here r=13, so subtract S12 from S24, not the other way around.