Problem Analysis #11

Kimi K3 · Run 1

Correct

5.24s

841 toks

API · no tools. This is the prompt and response recorded for this attempt; a full solution may not have been returned.

Problem Statement

This is a Korean CSAT mathematics multiple-choice problem. Solve it and put only the correct choice symbol, one of ①, ②, ③, ④, ⑤, inside \boxed{}.

Problem 12 Let{a n}be a geometric sequence satisfying 2(a1 +a 4 +a 7) =a 4 +a 7 +a 10 = 6. Determine the value ofa 10. [4 points] ① 22 7 ② 24 7 ③ 26 7 ④ 30 7 ⑤ 32 7

Ground Truth

②

Recorded model response / solution

Reasoning Process

Let the common ratio be $r$ . Since $a_4=a_1r^3,\ a_7=a_1r^6,\ a_{10}=a_1r^9$ ,

a_4+a_7+a_{10}=r^3(a_1+a_4+a_7).

From $2(a_1+a_4+a_7)=6$ , we get $a_1+a_4+a_7=3$ .
Then $a_4+a_7+a_{10}=6$ gives $3r^3=6$ , so $r^3=2$ .

Now

a_1(1+r^3+r^6)=a_1(1+2+4)=7a_1=3 \implies a_1=\frac37.

Thus

a_{10}=a_1r^9=\frac37\cdot (r^3)^3=\frac37\cdot 8=\frac{24}{7}.

\boxed{②}

Final Model Output

②

Comparative Analysis (P11) (Average across runs)

Averages use reported measurements only. Missing usage is not treated as zero.

Avg Time Taken

Motif 3

20.3

Solar Pro 4

11.2

Kimi K3

9.1

K-EXAONE-2

1.4

Avg Token Usage

Solar Pro 4

887.0

Kimi K3

859.7

K-EXAONE-2

626.7