In a book fair (27) books are sold at the first stall and (9) more books are sold at each next stall. How many books are sold at (13) stalls?

Correct answer: (1053)

The direct answer is C, 1053 books. The numbers form an arithmetic progression because the first number is 27 and the same number, 9, is added at every next stall. Thus the first term is a = 27, the common difference is d = 9, and the number of terms is n = 13. Use the sum formula: \(S_n=\frac{n}{2}[2a+(n-1)d]\). Substitution gives \(S_{13}=\frac{13}{2}[2(27)+12(9)]\). Now \(2(27)=54\), \(12(9)=108\), and \(54+108=162\). Therefore \(S_{13}=\frac{13}{2}\times162=13\times81=1053\). Option A, 1017, is too small and results from an incorrect total or term count. Option B, 1035, is also not the value of the required 13-term sum. Option C, 1053, matches the calculation and is correct. Option D, 1071, is too large, usually caused by adding one extra increase or using the wrong last term. Each stall represents one AP term, including the first stall. Exam cue: identify first term, common difference and number of terms before using the sum formula.