Answer:
1) is the only geometric sequence.
Geometric sequence is a sequence that has exponential behavior.
Step-by-step explanation:
You are looking for a common ratio.
That is you are trying to see which one produces the same number no matter what term you choose divided by it's previous term.
[tex]\frac{\text{ term}}{\text{previous term}}=\text{ same number }[/tex]
1) So we want to see if the following holds true. If it does, then it is geometric (has exponential behavior).
[tex]\frac{25}{5}=\frac{125}{25}=\frac{625}{125}[/tex]
Simplify:
[tex]5=5=5[/tex]
So one looks good.
2) [tex]\frac{18}{15}=\frac{21}{18}=\frac{24}{21}[/tex]
Reduce:
[tex]\frac{6}{5}=\frac{7}{6}=\frac{8}{7}[/tex]
These are obviously not the same number. Therefore, this is not geometric.
3) [tex]\frac{6}{3}=\frac{9}{6}=\frac{12}{9}[/tex]
The only integer is 6/3 which is 2 and the other two aren't so we don't have the same number across the board. Therefore, this one is not geometric.
4) [tex]\frac{16}{4}=\frac{32}{16}=\frac{64}{32}[/tex]
Simplify:
[tex]4=2=2[/tex]
Not the same across the board so this is not geometric either.
