API · no tools. This is the prompt and response recorded for this attempt; a full solution may not have been returned.
Token limit reached (8,192). The latest DeepInfra retry ended before a final answer was returned. This slot still counts as incorrect; the original timeout record is preserved.
This is a Korean CSAT mathematics numerical-answer problem. Solve it and put only the final integer value inside \boxed{}.
Problem 29 Let{a n}be an arithmetic sequence and{b n}a geometric sequence whose first terms and common difference/ratio are equal. They satisfy the following condition: For some natural numberk, bk+i = 1 ai −1 (i= 1,2,3). Suppose that the inequality 0< ∞X n=1 bn − 1 anan+1 <30 holds. Then a2 × ∞X n=1 b2n = q p , wherea 1 ̸= 0 andpandqare coprime natural numbers. Computep+q. [4 points]
No model response was recorded for this attempt.
Comparative Analysis (P36) (Average across runs)
Averages use reported measurements only. Missing usage is not treated as zero.