Question

find the common ratio \\(r\\) for the geometric sequence and use \\(r\\) to find the next three terms.

1. \\(-5, 20, -80, 320, ...\\)

first, identify each term in the sequence. for this sequence,
\\(f(1) = -5\\), \\(f(2) = 20\\), \\(f(3) = -80\\), and \\(f(4) = 320\\).
then, find the common ratio \\(r\\).
\\(r = \frac{\text{ }\text{ }}{\text{ }\text{ }} = \text{ }\text{ }\\)
lastly, use \\(f(n) = f(n - 1) \cdot r\\) with \\(r = \text{ }\text{ }\\) to find \\(f(5)\\), \\(f(6)\\), and \\(f(7)\\).

Explanation:

Calculate the common ratio r

Using the Common Ratio and Geometric Sequences knowledge points

$$ r = \frac{f(2)}{f(1)} = \frac{20}{-5} = -4 $$

Find the next three terms

Using the Geometric Sequences knowledge point

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Answer:

Find the common ratio \(r\) for the geometric sequence and use \(r\) to find the next three terms.

1. \(-5, 20, -80, 320, \dots\)

First, identify each term in the sequence. For this sequence,
\(f(1) = -5\), \(f(2) = 20\), \(f(3) = -80\), and \(f(4) = 320\).

Then, find the common ratio \(r\).
\(r =\) <blank>\(\frac{20}{-5}\)</blank> \(=\) <blank>\(-4\)</blank>

Lastly, use \(f(n) = f(n-1) \cdot r\) with \(r =\) <blank>\(-4\)</blank> to find \(f(5)\), \(f(6)\), and \(f(7)\).
\(f(5) =\) <blank>\(-1280\)</blank>
\(f(6) =\) <blank>\(5120\)</blank>
\(f(7) =\) <blank>\(-20480\)</blank>