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.
