If this is an arithmetic sequence, each of the terms will have a common difference. Let's check.
[tex]\begin{gathered} 3-21=-18 \\ 21-147=-126 \end{gathered}[/tex]
As we can see, each of the terms does not have a common difference. The first one is -18 while the other one is -126. Therefore, this is not an arithmetic sequence.
Now, let's check if this is a geometric sequence. If it is, each of the terms will have a common ratio.
[tex]\begin{gathered} 3\div21=\frac{1}{7} \\ 21\div147=\frac{1}{7} \end{gathered}[/tex]
As we can see, each of the terms has a common ratio which is 1/7. Therefore, 147, 21, 3 is a geometric sequence and the common ratio is equal to 7.
