If in an AP (S_{28}=2576) and (S_{14}=770), what is the sum from the (15)th term to the (28)th term?

Correct answer: (1806)

The direct answer is B: 1806. A partial sum S_n means the sum of the first n terms of the AP. The terms from the 15th through the 28th are exactly the first 28 terms after removing the first 14 terms. Therefore the required sum is S_{28}-S_{14}=2576-770=1806. Option A, 1778, is not the stated difference and is therefore incorrect. Option B, 1806, follows directly from the definition of partial sums. Option C, 1834, and option D, 1862, are also incorrect; they may come from adding or subtracting an extra term, but neither equals the sum of terms 15 to 28. No common difference or first term is needed here, because both relevant partial sums are already supplied. The key exam step is to check the endpoints carefully: subtract the sum through the term just before the starting term. Memory cue: terms m to n equal S_n-S_{m-1}.