Question

find the first four terms of the geometric sequence with \\(a_1 = 7\\) and \\(r = -2\\).
enter your answers separated by commas and surrounded by braces in the form \\(\\{a_1, a_2, a_3, a_4\\}\\) and in this order.

Explanation:

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<reasoning>

Identify the given parameters

\[

$$\begin{aligned} a_1 &= 7 \\ r &= -2 \end{aligned}$$

\]

Calculate the first four terms

\[

$$\begin{aligned} a_1 &= 7 \\ a_2 &= a_1 \cdot r = 7 \cdot (-2) = -14 \\ a_3 &= a_2 \cdot r = -14 \cdot (-2) = 28 \\ a_4 &= a_3 \cdot r = 28 \cdot (-2) = -56 \end{aligned}$$

\]

Format the sequence

\[
\{a_1, a_2, a_3, a_4\} = \{7, -14, 28, -56\}
\]
</reasoning>

<answer>
Find the first four terms of the geometric sequence with \(a_1 = 7\) and \(r = -2\). Enter your answers separated by commas and surrounded by braces in the form \(\{a_1, a_2, a_3, a_4\}\) and in this order. <blank>\(\{7, -14, 28, -56\}\)</blank>
</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Geometric Sequence"
]
}
</post_analysis>

Answer:

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"step_cot",
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],
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"Geometric Sequence",
"Common Ratio"
],
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}
</pre_analysis>

<reasoning>

Identify the given parameters

\[

$$\begin{aligned} a_1 &= 7 \\ r &= -2 \end{aligned}$$

\]

Calculate the first four terms

\[

$$\begin{aligned} a_1 &= 7 \\ a_2 &= a_1 \cdot r = 7 \cdot (-2) = -14 \\ a_3 &= a_2 \cdot r = -14 \cdot (-2) = 28 \\ a_4 &= a_3 \cdot r = 28 \cdot (-2) = -56 \end{aligned}$$

\]

Format the sequence

\[
\{a_1, a_2, a_3, a_4\} = \{7, -14, 28, -56\}
\]
</reasoning>

<answer>
Find the first four terms of the geometric sequence with \(a_1 = 7\) and \(r = -2\). Enter your answers separated by commas and surrounded by braces in the form \(\{a_1, a_2, a_3, a_4\}\) and in this order. <blank>\(\{7, -14, 28, -56\}\)</blank>
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Geometric Sequence"
]
}
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