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Answer:

1. The sequence is an arithmetic sequence since there's a common difference of 200 between the terms of the sequence.

2. The sequence is a geometric sequence since there's a common ratio of 4 between the terms of the sequence

Explanation:

In an arithmetic sequence, there will be a common difference(d) between the terms of the sequence.

While in a geometric sequence, there will be a common ratio between the terms of the sequence.

1) Given the below sequence;

[tex]-38,162,362,562,762[/tex]

Let's determine if the sequence above is an arithmetic or geometric sequence;

[tex]\begin{gathered} 162-(-38)=200 \\ 362-162=200 \\ 562-362=200 \\ 762-562=200 \\ \therefore common\text{ difference(d) = 200} \end{gathered}[/tex]

Since there's a common difference of 200 between the terms of the sequence, therefore, we can say that the sequence is an arithmetic sequence.

2) Given the below sequence;

[tex]2,8,32,128,512[/tex]

Let's determine if the sequence above is an arithmetic or geometric sequence;

[tex]\begin{gathered} \frac{8}{2}=4 \\ \frac{32}{8}=4 \\ \frac{128}{32}=4 \\ \frac{512}{128}=4 \\ \therefore common\text{ ratio(r) = 4} \end{gathered}[/tex]

Since there's a common ratio of 4 between the terms of the sequence, therefore, we can say that the sequence is a geometric sequence.

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