In an AP, (a=23), (d=9), and (n=26). Find the sum of the first (26) terms.

Correct answer: (3523)

The direct answer is option C: 3523. For an arithmetic progression, the sum of the first n terms is \\(S_n=\\frac{n}{2}[2a+(n-1)d]\\). Here the first term is a=23, the common difference is d=9, and the number of terms is n=26. First calculate n-1=25. Then calculate (n-1)d=25×9=225. Next calculate 2a=2×23=46. Add inside the bracket: 46+225=271. Finally, multiply by n/2: \\(S_{26}=\\frac{26}{2}×271=13×271=3523\\). Therefore option C is correct. Option A, 3487, is wrong because it results from an arithmetic or substitution error. Option B, 3505, is also incorrect because the bracketed total should be 271, not the value needed to produce 3505. Option C matches the complete calculation. Option D, 3541, is wrong because it is larger than the correctly calculated sum and usually comes from adding an extra amount or using the wrong difference. Another check is possible: the last term is \\(a_{26}=23+25×9=248\\); the average of first and last terms is \\((23+248)/2=135.5\\), and 26×135.5=3523. Exam cue: calculate (n-1)d separately and keep every bracket clear.