Question

given an arithmetic sequence with \\(a_1 = 16\\) and \\(a_4 = 25\\), find \\(a_5\\).

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Arithmetic Sequence"
],
"new_concepts": [],
"current_concepts": [
"Arithmetic Sequence"
]
}
</pre_analysis>

<reasoning>

Find the common difference

\[

$$\begin{aligned} a_n &= a_1 + (n - 1)d \\ a_4 &= a_1 + 3d \\ 25 &= 16 + 3d \\ 3d &= 9 \\ d &= 3 \end{aligned}$$

\]

Calculate the fifth term

\[

$$\begin{aligned} a_5 &= a_4 + d \\ a_5 &= 25 + 3 \\ a_5 &= 28 \end{aligned}$$

\]
</reasoning>

<answer>
28
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Arithmetic Sequence"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Arithmetic Sequence"
],
"new_concepts": [],
"current_concepts": [
"Arithmetic Sequence"
]
}
</pre_analysis>

<reasoning>

Find the common difference

\[

$$\begin{aligned} a_n &= a_1 + (n - 1)d \\ a_4 &= a_1 + 3d \\ 25 &= 16 + 3d \\ 3d &= 9 \\ d &= 3 \end{aligned}$$

\]

Calculate the fifth term

\[

$$\begin{aligned} a_5 &= a_4 + d \\ a_5 &= 25 + 3 \\ a_5 &= 28 \end{aligned}$$

\]
</reasoning>

<answer>
28
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Arithmetic Sequence"
]
}
</post_analysis>