Problem Analysis #18

Gemini 3.5 Flash · Run 1

Correct

2.88s

678 toks

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

Problem Statement

Return a single integer only. The problem has been revised so that no final answer is an irrational number, a parameterized expression, a range, a proof, a drawing, a graph, a locus equation, or a region description.

Let a sequence $(c_n)$ satisfy

c_2=2,\qquad c_3=4,

and for $n\ge4$ ,

c_n=c_{n-1}+c_{n-2}.

Find $c_6$ .

Ground Truth

Recorded model response / solution

Reasoning Process

To find $c_6$ , we use the given recurrence relation $c_n = c_{n-1} + c_{n-2}$ for $n \ge 4$ , starting with the given values $c_2 = 2$ and $c_3 = 4$ .

For $n = 4$ :

c_4 = c_3 + c_2 = 4 + 2 = 6

For $n = 5$ :

c_5 = c_4 + c_3 = 6 + 4 = 10

For $n = 6$ :

c_6 = c_5 + c_4 = 10 + 6 = 16

The value of $c_6$ is 16.

$\boxed{16}$

Final Model Output

Comparative Analysis (P18) (Average across runs)

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

Avg Time Taken

DeepSeek V4 Pro

5.0

K-EXAONE-236B-A23B

4.1

GPT-5.5

3.3

Gemini 3.5 Flash

3.0

Solar Pro 3

1.9

Claude Opus 4.8

1.6

KT Mi:dm 2.0 Base Instruct

0.7

Avg Token Usage